What are some possible reasons that my hands get numb after using a lawnmower or weedeater?

Carpal tunnel. It certainly could be carpal tunnel syndrome, a pinched nerve in your wrist which makes your fingers go numb. See a hand surgeon for an examination and treatment.
Many reasons. . There may be many reasons for this. One of the more common may be carpal tunnel syndrome, however to evaluate for and rule out more serious problems you should consider consultation with a neurologist.