=COUNTIFS(DATA!I:I,A4,DATA!G:G,"No",DATA!A:A,"*" & "2" & "*",DATA!C:C,"initial Review",DATA!L:L,"<>")
You should also be able to get rid of the ampersands and quotes around the 2:

=COUNTIFS(DATA!I:I,A4,DATA!G:G,"No",DATA!A:A,"*2*",DATA!C:C,"initial Review",DATA!L:L,"<>")

Note however, that wildcards don't work on numbers. So, if you're intention is to test for conditions like:

121
222
321

Then the wildcard criteria will not work.