You divide by two because you would be double counting otherwise.
J [img]/images/graemlins/club.gif[/img] J [img]/images/graemlins/heart.gif[/img] is the same as J [img]/images/graemlins/heart.gif[/img] J [img]/images/graemlins/club.gif[/img]. But 4x3 counts them both individually.
When order matters, it's called a permutation. When it doesn't, it's a combination.
With AK, it's (4x4)/2 = 8.
Permutations and combinations
explained.