For which of the following values of p, the mode of 4p−1, 2p, 4p−12, 3

If we take each answer choice and plug it into the given expressions (4p−1, 2p, 4p−12, 3p−1, and 2p+1), we see that most of them do not yield ANY values of 12.
For example, if p = 2, the expressions become: 4(2)−1, 2(2), 4(2)−12, 3(2)−1, and 2(2)+1
The expressions evaluate to be: 7, 4, -4, 5 and 5 {no 12's at all}

If p = 4, the expressions become: 4(4)−1, 2(4), 4(4)−12, 3(4)−1, and 2(4)+1
The expressions evaluate to be: 15, 8, 4, 11 and 9 {no 12's at all}

If p = 5, the expressions become: 4(5)−1, 2(5), 4(5)−12, 3(5)−1, and 2(5)+1
The expressions evaluate to be: 19, 10, 8, 14 and 11 {no 12's at all}

If p = 6, the expressions become: 4(6)−1, 2(6), 4(6)−12, 3(6)−1, and 2(6)+1
The expressions evaluate to be: 23, 12, 12, 17 and 13
AHA!! The mode here is 12

Answer: D

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