Moving kitchen sink in slab foundation
This should be achievable by adding a horizontal run from p trap to the drain without digging into your foundation.  Horizontal runs must be downwardly sloping at 1/4" drop per 1' run to function properly.
Since it sounds like you are only moving 8 inches you shouldn't need to worry about adding a vent line.  These are sometimes required by code for long horizontal runs and help vent gases allowing for smooth drainage.
The p trap can be on the front or back.  Doesn't matter as long as it does not become an s trap or a double p trap.