Push Down Automata

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I've been stuck on this one problem for a couple of days now with no clue on how to complete it.

Construct a PDA which accepts precisely the language $\{a^{2n} (bc)^n\mid n \in \mathbb{N}\}$.

If anyone can help. I would be eternally indebted

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HINT: Stack amber plates as they arrive. When a blue plate comes in followed by a *c(hartreuse plate, unstack two amber plates. Throw a tantrum if the amber plates don’t arrive in pairs, or the blue and chartreuse plates don’t alternate properly.