What is the "swap" trick, x% of y = y% of x, and why is it so useful?

You can flip which number is the percentage — because a%·b = (a·b)/100 = b%·a — turning a hard percentage into an easy one.

• 8% of 25 looks awkward → swap to 25% of 8 = a quarter of 8 = 2.
• 4% of 75 → 75% of 4 = 3.
• 18% of 50 → 50% of 18 = 9.

Both sides are literally the same product over 100, so the answer is identical — you just pick the orientation your head finds easier (often one side becomes "a half / quarter / tenth of a small number").