= Solution
For occupation numbers $n,m\geq0$, the Hamiltonian of the <two commensurate quantum harmonic oscillators> is
$$
H_0=N_A+2N_B+\frac32,
\qquad
E_{n,m}=n+2m+\frac32.
$$
The five lowest distinct levels and their product-state bases are
$$
\begin{array}{c|c|c}
E&\text{states }|n,m\rangle&\text{degeneracy}\\ \hline
\frac32&|0,0\rangle&1\\
\frac52&|1,0\rangle&1\\
\frac72&|2,0\rangle,|0,1\rangle&2\\
\frac92&|3,0\rangle,|1,1\rangle&2\\
\frac{11}2&|4,0\rangle,|2,1\rangle,|0,2\rangle&3
\end{array}
$$
The repeated levels exhibit <quantum degeneracy>.
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