When you come out at the top of the stairs, you should see a few zombines attacking antlion burrows in a garage structure. Move quickly, since one usually pulls out a grenade. Those still sting even if you’re behind the fence. Go to the end with your full shotgun and kill the first few antlions. Go to the center and use the gravity gun to knock the car into the burrow by the entrance to get a good start to the arena.
This antlion arena is a fairly tough area if you panic. I’ve actually seen Alyx die here, so that should give you an idea of the difficulty. You should be able to use the gravity gun to knock them onto their backs. Alyx seems to have a special kill combo for disabled antlions, so this is pretty effective. Go up the beam and turn around. If Alyx is surrounded, help her out. Then go forward through the narrow door with the supply box. Use the gravity gun to knock out the green car. Push it down into the pit and use it to block one of the burrows.
The battle gets a lot easier with just one burrow. Just pull out the shotgun and use it to keep them off your back. Go up the beams to the third floor. Look for the broken fence and go onto the ledge. Kill the zombine lying below and then drop down. Use the wheel to open the gate and then push the white car out into the pit. Use it to block the last burrow and end the fight.
Go back up to the third floor to the spot where Alyx should be waiting. Use the red wheel to open the side gate. Pick up the health packs and battery and then go down the steps. There’s a supply crate and half a zombie in the water at the bottom. Go down and kill it if you want more supplies. Go down the side room and into the shallow water. Go forward and help Alyx kill the 4 zombine that come at you. Then go by the pipes into the next area. Watch out though, since it looks like a zombine spawns behind you. Push forward and kill any stragglers and then go into the big room. Go ahead and grab the supplies to the right before you approach the elevator. This is the big fight for this chapter, so get ready.