4. Variant 1.

The numbers $96, 28, 6, 20$ were written on the board. One of them was multiplied, another was divided, a third was increased, and a fourth was decreased by the same number. As a result, all the numbers became equal to one number. Which one?
Answer: 24.

Solution: Addition and multiplication increase numbers, while subtraction and division decrease them, so the two larger numbers have decreased, and the smaller ones have increased. Now let's consider the two middle numbers 20 and 28. It is clear that a number was subtracted from 28, and the same number was added to 20. There can be no other options, because if you add a number to 6 and multiply 20 by the same number, the numbers will not be equal. The numbers became equal, and $28-20=8$, so both became equal to the number 24. Note that $96: 24=4,28-24=4,20+4=24,6 \cdot 4=24$. Therefore, the required number is 24.