twice the sum of number and 7 is equal to three times the difference of the number and 4

"the sum of a number and 7"  is  "x + 7"

So, "twice the sum of a number and 7"  is  2 · (x + 7)  =  2(x + 7)

"the difference of the number and 4"  is  "x - 4"  =  x - 4

The equation is:  2(x + 7)  =  x - 4

Multiply out:        2x + 14  =  x - 4

Subtract x from both sides:  x + 14  =  -4

Subtract 14 from both sides:  x  =  -18