How does Apollo help Hector kill Achilles' best friend, Patroklos?
Apollo is able to help Hector kill Patroklos because Patroklos ends up not listening to the advice that Achilles gave him prior to his departure into battle. Still fuming over his perceived slight from Agamemnon, Achilles warns Patroklos to save the burning ship and then return. Patroklos does so, but is an honorable warrior in his own right and proceeds on to Troy, thinking that with the momentum he has established, he can represent Achilles' armor well.
Apollo recognizes that the young soldier is out of his element. He is able to repel Patroklos and his men from the Trojan city walls. Apollo then hits Patroklos from behind, knocking off his armored helmet. From this, Patroklos is weakened and he retreats, taking injuries from the Trojans. This retreat is truncated when Hector sees the armored figure escaping, and thinking that it is Achilles, Hector is able to spear the warrior. Apollo helps Hector kill Patroklos, whom he thought was Achilles, by starting the process of weakening him and removing his momentum. When Apollo removes this momentum, Patroklos proves to be no match to the great warrior Hector and certainly less of a force than the man whose armor he donned, Achilles.