A chessboard is an 8×8 array of identically sized squares

A chessboard is an 8×8 array of identically sized squares. Each square has a particular designation, depending on its row and column. An L-shaped card, exactly the size of four squares on the chessboard, is laid on the chessboard as shown, covering exactly four squares. This L-shaped card can be moved around, rotated, and even picked up and turned over to give the mirror-image of an L. In how many different ways can this L-shaped card cover exactly four squares on the chessboard?

This problem refers to a figure in its source book that isn't reproduced here.

AQuA-RAT — Algebra Question Answering with Rationales (Ling et al., DeepMind, 2017) · train #14043