OPM 2023 Problem 3

A crate with a base of $4 \times 2$ and a height of $2$ is open at the top. Tomas wants to completely fill the crate with some of his cubes. It has $16$ equal cubes of volume $1$ and two equal cubes of volume $8$ . A cube of volume $1$ can only be placed on the top layer if the cube on the bottom layer has already been placed. In how many ways can Tom'as fill the box with cubes, placing them one by one?