Can someone please explain the intuition behind why we multiply the additional revenue (as a result of early recognition) by the gross profit margin to arrive at the answer? The question doesn’t mention anything about the GP margin. Confused.

It is just an algebraic shortcut, nothing fancy. It assumes the gross profit is constant, and given extra sales of 12m, how much of those sales made it to GP?

So imagine original sales=100 and COGS=47, the GP= 53. If you add 12m more sales, it is assumed extra COGS=5.64 (12 × 47%) so that the gross profit increases by 6.36 (12-5.64) becoming 59.36 (53+6.36). Thus the new GP is 59.36/112=53%.

Just to be clearer.