The engine is running lean, (too much air or not enough fuel) your palm is acting as the choke, lessening the amount of air able to enter the fuel air combustible mix.
remove and clean the carburetor, or if you want to chance a cheap amazon replacement carb, that is your choice to make.
also be sure you have good fuel flow to the carburetor from the tank.
if you can post the model and type numbers of the engine that would be great, so we can know what we're working with. if its a single cylinder usually stamped into the top or side of the valve cover.
