<...> he was very glad to see Rabbit getting out the plates and __ mugs.
Why there is an article before the first world and there is no article before the second one?
In this case, plates and mugs is a compound noun -- a single object made up of more than one thing. Some common examples are peanut butter and jelly, meat and potatoes, and song and dance.
What if we switched out plates and mugs for a simpler noun?
... he was very glad to see Rabbit getting out the dishes.
One could write the sentence as getting out the plates and the mugs, but that's a little awkward and repetitive. So, in this case, the author lumped them together as the one thing Rabbit was getting out.