What is the rule in hockey if an offensive player directs the puck with his glove on the defending goalie?
If the puck goes into the net, it is waved off as no goal, since a player can't propel the puck into the net with anything but their stick. It doesn't matter if the goalie touches it on its way in, as long as control of the puck isn't gained by anyone. Note that if it merely deflects off the player's glove and in, that's a good goal.
If it doesn't go in the net, and the first team to control it after the player batted it with his hand is his own teammate, then the play is whistled dead for a hand pass. You can't bat the puck to a teammate with your hand. You can bat the puck to yourself, though, so if the original player is the first to gain control, it's ok and play continues with no whistle.
If it doesn't go in and the defensive team is the first to control it, play continues like normal and nothing happens.
The goal counts as long as the player doesn’t kick the puck forward but if it bounces of the skate it is a goal