Correct Answer: $\frac{17}{8}$ and $\frac{15}{8}$

Solution : Given: $4^{(x+y)}=256$
⇒ $4^{(x+y)} = 4^4$
⇒ $x+y = 4$
⇒ $x = 4-y$-----(1)
And $(256)^{(x-y)}=4$
⇒ $(4^4)^{(x-y)}=4^1$
⇒ $4x-4y =1$-----(2)
Putting the value of $x$ from equation (1), we get,
$4(4-y)-4y = 1$
⇒ $16-4y-4y =1$
$\therefore y =\frac{15}{8}$
Now, substituting the value of $y$ in equation (1), we get,
$x = 4-\frac{15}{8}$
$\therefore x = \frac{17}{8}$
Hence, the correct answer is $\frac{17}{8}$ and $\frac{15}{8}$.