Try it. Two confining boxes can be described by two rectangular potentials, with walls at x=-L, x=+L, x=L+a and x=L+2a, for instance. Now try to solve the Schrödinger equation for the state of the two particles and see, whether entanglement can occur.
By studying the evolution of the two-particle state. Entanglement means that the probability distribution doesn't factorize as a unique product over the probability distributions of each particle.