Units digit

22^22 * 11^11  =

[ 2 * 11 ] ^22 * 11^11  =

2^22 *  11^22 * 11^33  =

2^22 *  11^33

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16    and repeats in a cycle of four

2^22 will end  in  a 4

11^any positive integer power ends in a 1

So

22^22 * 11^11   ends in  a  4