let 'x' and 'y' be the numbers and x>y

one number is six larger than another number

x = y + 6

the square of the larger number is 132 greater than the square of the smaller number.

x^2 = 132 + y^2

plug x = y + 6 into the previous equation

(y + 6)^2 = 132 + y^2

by solving we find

y = 8

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x = y + 6 = 8 + 6 = 14

the numbers are 14 and 8.