twelve decreased by twice a number is the same as 8 times the sum of number and 4. what is the number?

Let x be the number.

"twelve decreased by twice a number"   --->   12 - 2x

"8 times the sum of number and 4"   --->   8(x + 4)

12 - 2x  =  8(x + 4)

12 - 2x  =  8x + 32                    (distributive property)

12        =  10x + 32                   (add 2x to both sides)

-20       =  10x                           (subtract 32 from both sides)

x  =  -2                                      (divide both sides by 10)