This question wants you to choose the correct aspect based on the (supposedly funny) cartoon.
Oddly enough, I don't have a problem answering it, I just don't understand what it's asking!
Where is the joke?
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There's a common wisecrack I've heard, and it goes something like this:
Person A: I've been thinking...
Person B: Oh, so that's why I smell smoke.
Jokes like these are intended to compare the brain to some sort of mechanical device. Think too hard (the reasoning goes) and you might experience some sort of mechanical failure.
This cartoon plays off that line of logic. Apparently, Pembroke (and, as the commenters have said, that's just a name – it might as well be "Jones") has a reputation for being indecisive, to the point where his head "explodes" when he needs to make a decision. In this case, a co-worker is making a casual observation of the aftermath.
I understand the comic, but I don't find it hilariously funny. It's mildly amusing at best, and could be labeled as dry humor.
I checked out the word Pembroke in Wikipedia and found this:
The town and county derive their names from the cantref of Penfro: Pen = "head" or "end", and bro = "region", "country", "land", which has been interpreted to mean either "Land's End" or "headland"
Pembroke is just a name, it has no other significance.
Any humour in the cartoon will come from knowledge of the character over time in a regular comic strip. I can't speak for others but the frame presented contains no comedic elements.
It's likely from their clothing that Pembroke is some middle-manager who has no real decision-making power but will bear the responsibility for making their bosses' poorly thought out schemes work, but that's entirely a guess.