Which of the following numbers will completely divide $4^{12}+4^{13}+4^{14}+4^{15}$?

Let the given expression be $E$:
$$E=4^{12}+4^{13}+4^{14}+4^{15}$$
Take out the common factor $4^{12}$:
$$E=4^{12}(1+4^1+4^2+4^3)$$
$$E=4^{12}(1+4+16+64)$$
$$E=4^{12}(85)$$
We can rewrite $85$ as $5\times 17$:
$$E=4^{12}\times 5\times 17$$
Since $17$ is a factor of the expression, the expression is completely divisible by $17$.