The fact that it's possible know whether a man went to hell or to heaven is testified by the word of God by the Lord Jesus Christ Himself:
22 And it came to pass, that the beggar died, and that he was carried away by the angels into Abraham's bosom: and the rich man also died, and was buried.
23 And in Hades he lifted up his eyes, being in torments, and seeth Abraham afar off, and Lazarus in his bosom.
This is also confirmed by the Tradition of the Church which includes empirical testimonies of holy pleasers of God.
In our daily life it is possible for us to know if God blesses us with a revelation of a certain person's destiny after their death. It is done not to satisfy idle curiosity but to certify (if it's helpful) of a soul's destiny, in order to pray for it and for other important reasons.
In our congregation we have a recent example from our life in 2002. During the great Fast I was addressed, by means of our site, by a servant of God, Victor Perepelitsa who lived in Toronto. He had searched for God, had been sprinkled in a temple of the "MP" and was attending the "MP"'s temple in Toronto. His soul wasn't satisfied with it and the priest hadn't been able to answer his questions (although boasting that he had been teaching in a spiritual academy for 20 years). When Victor read materials on our site, his soul, said he, opened up in a sense and he grasped the truth. The attracting grace fell upon him. Under its influence he addressed me and we met. He had the 4th stage of cancer (black cancer) with metastasis in his liver, legs and other parts of his body. I received his confession and baptized him in a lake on the Great Saturday and the great grace of baptism came upon him. I performed the mystery of chrismation in the temple and declared him a member of the Church. It was obvious to everyone that the great converting grace had come upon him because of which he was just glowing. His health condition also considerably improved. He wholeheartedly clung to the Lord, to the Church and to me, a shepherd of the Church.
The Lord allowed him to experience different states of grace. He experienced what it is like to pray without a thought, he felt what it's like to be cut to the heart, he cried, he had the vision of sin and the feeling of repentance. Victor asked me to reveal to me his destiny from God, whatever it could be. I prayed and it came to me from God that he would soon pass away to the Kingdom of heaven. I told all my parishioners about it and that he didn't have even one year. One day, after the liturgy, he again asked me about it and I told him all the truth. He gave God thanks and began preparations. Victor always loved to go everywhere with me and always asked me to take him with me. That autumn I was going to pilgrimize to Greece. Victor also wanted to go, but an exacerbation of his leg disease didn't allow him to go. His pains had gone more intense and he took to his bed. I visited him before leaving, received his confession, served him the Eucharist and aneled him and left with him several particles of spare sacraments to partake of the Eucharist in my absence. He was begging me to pray for the Lord to help his soul to be delivered from his body for he had to undergo an amputation of both of his legs, to take narcotic medicine, to face agony and difficult death. I performed a rite for the seriously sick with long-lasting diseases when they cannot die, and promised Victor that he would have passed away by my return.
On the 1st (14th according to the New Style) of October, on the day of the Cover of the Holy Mother of God he called me in Greece and told me that everything was without any changes, he was still hurting. I asked him to have patience yet for a short while. I was constantly praying for his deliverance from the chains of his suffering flesh. On the day of the Cover my wife and I and brother Mikhail visited several temples where I prayed for that. In a deserted ancient monastery (used as a parish), where the wonder-working icon of the Mother of God is, I was just talking in front of it with the Most Holy Mother of God, asking Her to help brother Victor to be delivered. On the 2nd (15th according to the New Style) of October he partook of the Sacraments and had an apoplexy in the morning, of which he died. I was told about it by phone and I went to the church of John the Divine and performed a rite of absentee burial service. Then we changed the tickets' dates without any extra fee (which was impossible) and flew to Toronto. On the 8th (21st New Style) of October I performed the rite of burial service and funeral of brother Victor. At the moment of the funeral the sun came out and sent a bright light ray to the casket when it was being lowered into the tomb. During all the burial service the attending people's hearts were filled with quiet joy. I had no doubt in a good Victor's destiny after his death.
On a late evening of the eve of the 1st of January, brother Victor's soul visited me as a waking vision. At the time there were my wife and three other people from the congregation. I was the only one who saw and heard Victor (in the spirit). My conversation with him was overheard by everyone in attendance. He told me that he was in an unspoken beautiful place of the Kingdom of heaven and thanked me for helping him in the work of his salvation. The vision lasted for 1-2 minutes and he left. Thus we received the confirmation of his eternal destiny (I had asked him to come back if the Lord allowed). I had seen similar things before (seldom). My wife's brother (his soul) had come, the singer Igor Talkov (his soul) was beseeching my prayers, my classmate (who had died from radiation in Chernobyl) came for four times, Father Georgiy, a priest (who died for the sin of serving the Eucharist to the parishioner who had been unchurched by me, who I was upset with and had not prayed for before visiting him). I not only knew these souls' destiny but also knew how it was being changed through the prayers of the Church (souls from hell were transferred to heaven).
Praise be to our God Who is wonderful in His mercy!