OR is a logical (or boolean) operation - it expects a condition on either side.
So this would work:
SELECT SerialNo FROM necessitycompdetail
WHERE VehicleNo = 'CG04JC7882'
AND (Activity = 'REMOVE' OR Activity = 'NEW ISSUE')
But I'm not sure exactly what you are trying to do: are you trying to get tyres which have not been removed - perhaps a list of what you want to get from your sample data would help?