When can the order of boolean operations be exchanged? Is there an easier way?

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Suppose that we have two binary boolean operators $\circ$ and $\star$ (not necessarily different). Now in general $(A\circ B) \star C = A \circ (B\star C)$ doesn't hold, but certainly sometimes it does.

Now my question was for which choices of $\circ$ and $\star$ the equation holds? Of course one could just figure out using brute force and just iterate through all combos and do truth tables and find the combos that work out (I've got $58$ of them).

Isn't there an "easier" way of doing this? Something that could feasibly be proved on paper?