since Sherman tank come with different variant,which variant of Sherman tank use in normandy and italy?

Nearly whatever one you want to build a version of it was used in Normandy and Anzio except the M4A3.

M4 75mm
M4 105mm (arrived just in time for Cobra like the M4A1 76mm)
M4 composites and IC Fireflies
M4A1 (the whole array from the direct vision first production in Italy to the remanfuactured and late production and the 76mm in Normandy.)
M4A2 75mm (British and Free French)
M4A3 (really post-Normandy and Anzio only arriving in early fall of 1944)
M4A4 (Canadians in Italy, main commonwealth and Free Polish in Normandy) and main version used for Fireflies.

To be more specific for Anzio early M4 and M4A1 were still standard with the Americans and the Commonwealth had M4A2 and M4A4. (Sherman III and V)

M4A3 are the only ones which really post-date use in both Normandy and Anzio.

Could you be a little more specific? Which units? Which countries even?

Stephen has summed it up very well. In the British and Commonwealth units there were tanks still fitted with the M3 VVSS in use.

Small numbers of M4A3's were used during the later stage of the breakout and the drive on Paris. As Stephen said, not really Normandy in the pure sense. If you expand your theater to France then the M4A3 becomes more common.

Thank's for the info!