Answer
$CH_4$ is neither acid nor base.
Work Step by Step
$CH_4$ can't be a base, because it doesn't have a lone pair of electrons.
It is a very weak acid, so we don't even consider it one, because $CH_4$ isn't capable of changing the pH or the $[H_3O^+]$ of a solution significantly.
$K_a < 10^{-14}$
