If HOUSES = GNAYDR, then DIARY =

In HOUSES → GNAYDR, the first two and last two letters each move one step back (H→G, O→N, E→D, S→R), while the middle two move six steps forward (U→A, S→Y). DIARY has five letters, so the first two and last two move back and the middle one moves forward: D→C, I→H, A→G, R→X, Y→X, giving CHGXX.