In a lot of 2,500 bulbs, 8% failed the first check, and 4% of the bulbs that passed the first check failed the second. How many bulbs cleared both checks?

After the first check, 92% of 2500 = 2,300 bulbs survive. Of these, 96% clear the second check: $2300\times 0.96=2,208$. 2,300 stops after the first check. 2,200 is $2500\times 0.88$, from adding the two failure rates into a single 12% - but the 4% applies only to the 2,300 survivors, not to all 2,500. 2,400 applies the 4% alone.