We show that K-moduli spaces of (P^3, cS) where S is a quartic surface interpolates between the GIT moduli space and the Baily-Borel compactification as c varies in (0,1). We completely describe the wall crossings of these K-moduli spaces. As a consequence, we verify Laza-O'Grady's prediction on the Hassett-Keel-Looijenga program for quartic K3 surfaces. This is based on joint work with K. Ascher and K. DeVleming. Speaker(s): Yuchen Liu (Northwestern University)