Maybe someone's order from King's game (truth or dare) perhaps? Well in any case, poor Haguro carrying Yamato is a overkill with that weight difference. It's a miracle she even managed to lift her at all.
I know this is a bit late, but fun fact, while Yamato did famously fly the Z flag, when flown otherwise it means the vessel needs a tow/tug. Maybe the artist was making a pun off of that.
Thing is, Haguro could probably manage the tow (though not piggyback like this :D ).
Sure, Yamato's displacement was far greater, but Haguro wouldn't have to *lift* Yamato, just drag her along. So it's engine power that you need to compare, not displacement.
Yamato's engine power was 150,000 horsepower for her designed speed of 27 knots. Haguro's engine power was only a little less, 130,000 horsepower, for her designed speed of 35.5 knots. Unlike most battleships (the Iowas being the really notable exception), cruisers are all about speed, and therefore have lots of engine power for their relatively low displacement.
At the much lower speed required to tow Yamato, Haguro would need far less than her full power to move her own hull, so much of her power could be applied to moving Yamato's bulk. Haguro would have to work hard, sure, and I'm not sure how efficient her screws would be when applying maximum power at far less than maximum speed, but it still seems like a feasible task.
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