You'll enter a warehouse area. Follow the little path and then crouch under the shelves to move along further. Half of a fast zombie should move toward you, so blast him. There should be a barnacle covering the exit. Use the gravity gun to feed it a barrel, then crawl out. There's another half zombie in here. Just nail him with a barrel.

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You need to get up on the first shelf and then follow the makeshift stairs up and around until you get to the gap. Just jump and press against the next “step” to get up. You should come to a forklift. Kill the black headcrab that drops down and then jump down to the forklift. Put a barrel on it and then flip the switch. Quickly jump on and ride it up. You can stand up on the barrel and use it to jump up onto the tall shelf in front of you.
Break out the grate and crawl through the vents until you get back out in fresh air. Drop down the hole using the pipes as steps. Then just move on forward to the toxic wastes.
You don't need the pallets for this part. Just jump correctly. Alyx should be able to snipe most of the zombies that pop up, but you should really keep your shotgun out to take out anything that emerges in her blind spot or gets too close. Jump from raised garbage patch to garbage patch and then follow the left wall. Kill any new zombies that spawn, since Alyx won't have a shot in the back corner. Move over and jump up onto the little wall, and then get behind the fence. Blow up the barrel as the group of zombies move toward you. Then clear a path forward and up to the ammo crate. Get some more SMG grenades. You might as well get them.