Dude, are your pants down around your ankles? cuz someones trying to screw you.
let me help.
Draw you lines on the floor, make the hole 4 in larger on each side, this is so you can Turn down the slab for a finished look, remove as much gravel as needed to give you the proper drop needed plus 4+ inches of concrete. for strength, drill some hole along the side to let in some short pcs of rebar, 3/8 should work fine, have them come into the now new slab a couple in and then turn down to below the top of the new bottom slab. make sure to lay some 6mil plastic down, as a moisture barrier.
you will need to form the new edge, pour that and wreck the form and then pour the bottom.
If you send me a picture of existing conditions and size wanted for the lift, I can draw it up for you.
this whole thing should not cost more than 800 all in.