Tips & strategy
Look for the factor pairs of 24 first. Three times eight, four times six, and twelve times two are the usual routes, so ask whether you can build one of those numbers from the others rather than working forward blindly.
Do not avoid division. Beginners stick to adding and multiplying, but many hands only work if you divide somewhere, sometimes producing a fraction that resolves later. Being willing to make an odd intermediate value is what unlocks hard sets.
Try subtracting to reach a useful number. If you have a large number, subtracting your way down to six or eight and then multiplying is often easier than attacking 24 directly.
Work backward from 24. Ask what pair of numbers would give you 24, then whether your remaining values can produce them. That is usually faster than exploring every combination forward.