  Inspired by the ideas of the minimal model program, Shepherd-Barron,
Koll\'ar, and Alexeev have constructed a geometric compactification for the
moduli space of surfaces of log general type. In this paper, we discuss one of
the simplest examples that fits into this framework: the case of pairs (X,H)
consisting of a degree two K3 surface X and an ample divisor H. Specifically,
we construct and describe explicitly a geometric compactification $\bar{P_2}$
for the moduli of degree two K3 pairs. This compactification has a natural
forgetful map to the Baily-Borel compactification of the moduli space $F_2$ of
degree two K3 surfaces. Using this map and the modular meaning of $\bar{P_2}$,
we obtain a better understanding of the geometry of the standard
compactifications of $F_2$.
