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I guess for them it would be more like a three - four with the leading one - digit number, would it not? Did they have a 60 x 60 multiplication table at hand? I am almost tempted to try it out, I would guess that it should be doable in two hours in modern notation.

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I assume it was in their head.

I don't know exactly how large of a times table I have in my head, but it's larger than 10x10, more like 15x15. A 60x60 table is 16 times larger than that, but I also learned my times table in elementary school and being a scribe or whatever the job title was for a guy who multiplied was very likely a full time job for a grown Babylonian. Learning your times tables up to 60x60 seems totally plausible.

We know that by 300bc at the latest that they had abacuses, so I imagine they used these

Sumerians invented it circa 2800-2500BC. 300bc is a thousand years after the tablet in question. I believe the oldest extant example is 300bc.

15x15 plus 10xInfinity ;-)

There's some other odd ones like 16x16 but the table gets pretty sparse after the 15's.

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