Twice the sum of a number and 6 is equal to three times the difference of the number 6. find the number

Set up an equation like this, where n represents the number:

2(n + 6) = 3(n - 6)

2n + 12 = 3n - 18

-n + 12 = -18

-n = -30

n = 30

The number is 30.  You can even double-check by plugging 30 into each side of the original equation and simplifying:

2(n + 6) = 3(n - 6)

2(30 + 6) = 3(30 - 6)

2(36) = 3(24)

72 = 72

Check.

2(n+6)=3(n-6)
2n+12=3n-18
12=1n-18
-6=1n
n=-6