How much compression is made in a predator 212 when a high compression head and thinner head gasket is added?

Depends on actual parts numbers, actual gasket. 6.5 to 1 compression ratio may be regular ratio now for the Predator which is Harbor Freight, Mainland Chinese made Honda copy. 5.5/ 6:1 was about normal in old leaded fuel days with no emissions laws. Where are you getting the 'High compression' head? after market Go-Kart supplier or the factory LP gas head for some markets? LP heads are about 1 to 1.5 higher compression to maintain power with the lower energy content CNG/ LP gas fuels. Old Kohler gasoline generator engine was 6:1, the LP head was 7.5 to 1 . Thin Gasket? soft copper sheet has been used for head gaskets at times, O rings with machine relief in heads another way for gasketing getting higher compression, soft Aluminum home made from beer cans has been done. some shop work may get you higher compression- mill/ flatten top of cylinder level with a .1mm / .004 thousands cut, same on bottom of head and then thin soft copper gasket or in a few cases a coating of aluminum paint or Coppercoat paste gasket maker. need to carefully adjust valve lash- try .006 to 008 thousands and listen for heavy valve tick to start, very light tick when warm. Have fun, Predator engines on sale are $99.00 so relatively cheap to hot rod for go-Kart and Mini bike use.