If we believe in Jesus, we will do greater works than He did because of the power of prayer which He has given us (Jn 14:12-13). Jesus promised: "Whatever you ask in My name I will do, so as to glorify the Father in the Son. Anything you ask Me in My name I will do" (Jn 14:13-14). If Jesus puts His name on our prayer, then the prayer is answered as we have requested. In other words, if we pray according to His will, not ours, what we pray is what will happen. If we seek first the kingdom of God, everything will be given us besides (Mt 6:33).
If we pray to be healed from cancer, will Jesus put His name on this prayer and will we be healed? Although the Lord usually wants us to be healed, and was even wounded so that we may be healed (1 Pt 2:24), healing is not the Lord's highest priority. Therefore, the Lord may or may not put His name on our prayer to be healed from cancer. However, if we prayed to have the health necessary to witness for Him and to build His kingdom, then the Lord would put His name on that prayer. We may then be healed, or we would be able to do what the Lord wants us to do, even if we're not healed. When we pray for Jesus' prayers to be answered, then that prayer is answered. Pray in Jesus' name.