lawnmower stalls

I have an old snapper self propelled lawnmower. This season when mowing, the lawnmower stall if I am on a hill, and the lawnmover is leaning to my right (my right while I am walking behind the mower, towards the side where the gas cap and oil cap are located). When I am leaning in the other direction, however, there is no problem. The angle of the slope doesn't have to be much more than a few degrees to cause the problem. After it stalls, it is very difficult to get started again.
Any ideas what the problem is?

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