Let us "translate" the words into algebra, step by step:
x = the number
Difference of a number and 2: (x - 2)
Eight times the difference of a number and 2: 8(x - 2)
The sum of the number and 3: (x + 3)
Three times the sum of the number and 3: 3(x + 3)
Eight times the difference of a number and 2 is the same as 3 times the sum of the number and 3:
8(x - 2) = 3(x + 3)
Now just solve for x.
8x - 16 = 3x + 9
5x = 25
x = 5
The number is x = 5