The deep palmar veins drain into the radial and ulnar veins; then those veins, along with the anterior crural interosseous vein, drain into which vein?

Brachial vein.

Explanation:

Veins may be defined as the blood vessels that carries the blood towards the heart. The main function of the vein is to carry the deoxygenated blood into the heart.

Brachial vein is the deep veins that has the name as their arteries occupy. The brachial veins receive their blood from the palmar veins with the interosseous vein. The brachial veins include the ulnar vein, radial vein in upper limb and lower limb consists of popliteal veins.

Thus, the answer is brachial veins.