Starting from the top.
Some primers squirt fuel directly into the carb
Other depress the float to raise the fuel level
So we need to know the full engine number which will be on the rocker cover or the heat shield above the muffler.
Next if it is an OHV model, check the valve lash.
If it starts easily with fuel dumped into the spark plug hole & does not start easily with fuel dumped into the carb then check the long manifold that the carb sits on.
IT goes all the way across the engine and is prone to cracking