The number of four-digit numbers that can be formed using distinct digits from \1,2,3,4,5\ and are divisible by 4 is

A number is divisible by $4$ exactly when its last two digits form a multiple of $4$. Two-digit multiples of $4$ with digits from $\{1,\dots,5\}$ are $12,\,24,\,32,\,44,\,52$. The pair $44$ repeats a digit, so it is not allowed, leaving $4$ valid endings. For each ending, the first two places are filled from the remaining $3$ digits in $3\times2=6$ ways. Hence the count is $4\times6=24$. Counting $44$ would give the trap value $30$.