Why is adenine aromatic? I don't think it follows the $4n + 2$ rule. The double bonds give 8 π electrons. Then the lone pairs on the $\ce{NH}$ and $\ce{NH2}$ groups are delocalized (are they?) so they must contribute 4 π electrons. Thus in total there are 12 π electrons, which doesn't follow Hückel's rule. So, why is it aromatic?
The $4n+2$ rule applies only for a conjugated ring.  If you assume that the amino group contributes a pair of pendant  $\pi$ electrons into the ring system then perforce you do not have a conjugated ring.  And even if you don't assume such a delocalization from the amino group, the cross-link within the ring system is still a stretch for the $4n+2$ rule.