If I have a Conkeldurr with Drain Punch and Mach Punch, can I breed those moves as egg moves with a Ditto?
If this is about X/Y, yes because as of X/Y both parents can pass down egg moves.
Note- Ditto can't pass down egg moves, since the only move it can learn is Transform.
Source - Bulbapedia and experience.
In X/Y, Yes in any other gen No. This is because in Pokemon x/y because both Pokemon pass down their egg moves. But please note that this will not work with ditto! If you want to pass these down you must use a Pokemon in Human-Like breeding group! Also please note that the Pokemon your trying to breed with must be able to learn the moves you are trying to pass down! You can check on their page right here if they can learn it as an egg move. Hope this helped!