Backhopping forwards is a move in the sport of bicycle trials. It's similar in theory to backhopping, except that because you're trying to move forwards it's much harder to learn in practice, and actually uses a completely different motion to backhopping. To learn to backhop forwards, I would recommend to first read backhoping and learn to do it a least 8-9 times in a row, preferably 10-12. But while you're doing all this practice try to think about what you actually need to do to go forwards. Now that you can backhop without any particular effort you're ready to learn to backhop forwards.
The first thing to remember is that because you're travelling in the opposite direction you need to reverse the motions you're doing. First of all, try to keep your front wheel only slightly above the ground, a foot above at most. Next, reverse the tilt of your feet so that your toes are above you heel. Now, instead of pulling back and up you're going to have to push forwards and up, which is why you reverse the tilt of your feet. Also, try to pull up the front wheel, so you go from your front wheel only slightly above the ground to almost straight above the back wheel. Basically you're pulling the bike up and yourself down.
Backhopping forwards is something that requires a lot of coordination and practice. While it might seem impossible at first just keep practicing and pay a lot of attention to how your body is moving. Remember, once you learn to do this move it opens up all sorts of terrain that has been previously unrideable.
Happy riding, and if you have any questions of comments just message me.