I just repaired the engine on my Yard Machine. I re-installed it using the same mounting holes and now the transmission drive belt is way too loose and I can't figure it out.

If you have it in park or brake set it will be loose.
Check your other pulleys make sure the belt is on those correctly
When you start it the variater pulley may tighten it.Luck

"same mounting holes " that catught my eye, what did you unbolt? Changing that belt usually does not require removing anything. Tell us how you removed the belt. Did you have the spring loaded tensioner arm pulled back so that it presses on the belt to create tension when you let go of it?