Final answer:
None of the expressions provided have a value of 4 when evaluated correctly. Therefore, there might be a mistake in the given options, or none of the given expressions is meant to equal 4.
Step-by-step explanation:
The student has asked which expression has a value of 4. We need to evaluate each expression to find out which one equals 4:
12 = 22 + 2 does not equal 4; this is clearly incorrect as the right side equals 24.
24 = (2 + 1) - 22 also does not equal 4; the right side simplifies to 3 - 4, which equals -1.
16 = (1 + 1)^2 - 1 does equal 4; (1 + 1)^2 is 2^2, which is 4, and 4 - 1 is indeed 3, not 4.
36 = (2 + 2) - 32; the right side simplifies to 4 - 9, which equals -5.
After evaluating the expressions, none of them has a value of 4. Therefore, there might have been a mistake or typo in the original options provided. If these were meant to be equations, then all of them are incorrect as none of the expressions on the right-hand side equal the numbers on the left-hand side.