You are correct. The answer is b = -6
The rules used here are
- (a^b)^c = a^(b*c) ... multiply exponents, base stays the same
- a^(-b) = 1/(a^b) .... use reciprocal to get the exponent positive
The first rule mentioned has us multiply the exponents b and 4 to get 4b. Then use the second rule to turn 1/(y^24) into y^(-24). So we can see that 4b = -24 leads to b = -6 after dividing both sides by 4.