the two consecutive integers can be written as:

x and x + 1, where x is integer

x + 1 > x that is x + 1 is the greater integer

the product of two consecutive integers is 12 less than the square of the lesser integer:

x(x + 1) = x^2 - 12

by solving we find:

x = -12

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x + 1 = -12 + 1 = -11

the greater of the two integers is -11.