Does a pair of aces and a pair of two beat a pair of kings and a pair of eight?

No, the higher ranking pairs in each hand have priority and are compared first and a pair of Aces beats a pair of Kings.

The value of the lower pair is only relevant if the higher pairs in each hand are the same, for example KQ v K7. In this example the lower ranking pairs in each hand would be compared and because a Queen is higher than a seven, KQ beats K7.