Question 2853
You have all the information you need from the question itself.

Let the numbers be x,y.

"One number is two times another."

Then, x=2y ..................... [Statement 1]


Now y is half of x (from statement 1).
Therefore x>y.

"Eight times the smaller is two more than twice the larger number."

Then, 8y =  2x + 2 .....................[Statement 2]

Substituting (x=2y) in the second equation we get,

8y = 2(2y) + 2
8y = 4y + 2
8y - 4y = 2
4y = 2
y = (2/4)

Therefore, y=1/2

x=2y => x=2(1/2) => x=1

Therefore we get,
x=1
y=(1/2)

Solution crosscheck:
Puttting these solved values of x and y in the 2nd equation we get,
8(1/2) = 2(1) + 2
4 = 2 + 2
4 = 4

As Lefthand side (LHS) and Righthand side (RHS) are equal,
solved values of x and y are correct.

Hope this helps,
Best of luck.