How to find number of 4 digit numbers divisible by 4 that can be obtained using 1,2,3,4,5,6 with no numbers repeating?
For non-repeating: number is divisible by 4 iff its last two digits are divisible by 4. IN your case, it will be 12 16 24 32 36 52 56 64
So you have 8 possible endings.
First two digits can be chosen in 4 * 3 ways, so overall answer will be 12 * 8 = 96
[This is an answer to the original question, in which repetition was not excluded.]
For the number to be divisible by $4$, the number formed by the last two digits must be divisible by $4$. With the digits $1$ through $6$, you can use the $3$ last digits $2$, $4$ and $6$, and each of these can be combined with half of the digits to form a $2$-digit number divisible by $4$, so there are $9$ combinations for the last two digits. The other two digits can be chosen arbitrarily, so there are $36$ combinations for those, for a total of $9\cdot 36=324$ different numbers.