How many 4-digit numbers that are divisible by 4 can be formed...

A number is divisible by $4$ if the number formed by its last two digits is divisible by $4$.

Using the digits $1, 2, 3, 4$ without repetition, the possible two-digit numbers at the end that are divisible by $4$ are $12, 24$, and $32$.

For each of these endings, the remaining two digits can be arranged in the first two places in $2! = 2$ ways.

Total number of such $4$-digit numbers is $3 \times 2 = 6$.

Answer: $6$