Answer
$a)$ $(4,12)$
$b)$ $(8,16)$
Work Step by Step
$a)$ $f(x+4)$ is horizontal translation of $f(x)$ by $4$ units to the left.
Points on it will move $4$ units to the left as well:
$$(8,12)\rightarrow(8-4,12)=(4,12)$$
$b)$ $f(x)+4$ is vertical translation of $f(x)$ by $4$ units up.
Points on it will move $4$ units up as well:
$$(8,12)\rightarrow(8,12+4)=(8,16)$$
