The question you opened
Boxes on a full truck
A pallet holds 24 boxes and the truck takes 36 pallets.
How many boxes fit in one truck?
864 boxes
Split 36 into 30 and 6. Twenty four times 30 is 720, twenty four times 6 is 144, and the two parts add to 864.
Twenty four times 36 is 864. The reliable route is to break the second factor: 36 is 30 plus 6. Twenty four times 30 is 720, because 24 times 3 is 72 and a zero follows. Twenty four times 6 is 144. Adding 720 and 144 gives 864. This is the distributive property, and it is the backbone of every mental multiplication method that works under pressure. Written multiplication asks you to hold carries in a fixed order.
Splitting asks you to hold two clean numbers and add them, which is far easier to do while someone is talking. Which split to choose depends on the numbers. Round down is usually best: 36 into 30 and 6, 47 into 40 and 7, 68 into 70 minus 2. That last form matters, because subtracting is often easier than adding. Twenty four times 68 is 24 times 70 minus 24 times 2, so 1,680 minus 48, which is 1,632.
A second route exists here and is worth seeing. Twenty four times 36 is also 24 times 6 times 6, so 144 times 6, which is 864. Factoring one number into smaller pieces turns one hard multiplication into two easy ones, and it works whenever a factor has small divisors. A third route uses the fact that 24 and 36 are both multiples of 12.
Twelve times 12 is 144, and 2 times 3 is 6, so the product is 144 times 6 again. Spotting a shared factor is the fastest of the three when it is there. The practical part is the checking. The answer must end in 4, since 4 times 6 does, and it should sit near 25 times 36, which is 900. Both checks pass, which is enough confidence to say a number out loud.
Technique: Split 36 into 30 and 6