Rip a 2x8 to 6" and toe nail it on the flat to the wall studs just below the top of the cabinets. Hot melt a little blocking to hold it until you screw the cabinets to it.

you simply need a continuous cleat on the wall, no real need for the "on center" portions. One or two could be used to keep the assembly from movung during top install though.

A 2x4 is good but you need to select a very straight one - at least on one edge. You could make the cleat outa 3/4" plywood strips too. This would take care of the straight aspect, but is a bit more work.

Being the super cautious guy that I am, and knowing that base cabinets are designed to be screwed to the wall, I would probably build out a ledger to 6" at the top of the cabinets and screw a cleat to the floor 6" out to support the bottom of the cabinets. Probably not necessary, but simple to do and it might save problem later on if someone give the boxes a good kick.

But, why not just use 30" deep cabinets. They are no harder to build than 24" deep cabinets and provide 25% more storage -- always welcome in a kitchen.

Here's a row of 30" cabinet we built for a customer. Even with 12" appliance garages, there is still 19" of working space on the countertop, which is a useful amount of space.

The deeper drawers are also very handy.

I second building 30" deep cabinets. Why waste that valuable space? Drawer glides come in various lengths to accommodate deeper drawers.

Just wanted to throw this idea out (maybe crazy talk) but I was thinking about a 2x6 knee wall with 1/2" sheathing on the face. Total stack up would be 5 1/2 + 1/2 = 6". Vertical studs could be 2x4's, to save a little money, and top and base plates be 2x6....just a thought