Why does a Briggs Stratton 6.75 lawn mower engine not restart when ho t?

This is called a "hot restart problem" and is commonly caused by vapor lock, which is the accumulation of air bubbles around the main jet, emulsion tube, etc. Most immediate solution is cleaning and rebuilding of the carburetor, particularly the bowl vent and main air bleed. An alternative would be to lean out the mixture via the needle valve, if equipped.