The sum of two numbers is twice their difference. the larger number is 6 more than twice the smaller. find the numbers.

Let the numbers be x and y; x being the larger number and y being the smaller.

Given,

x + y = 2 * (x - y)

x + y = 2x - 2y

x = 3y

Also given,

x = 6 + 2y

3y = 6 + 2y

- - - y = 6

Thus, x = 3y = 3*6 = 18.

Therefore, the numbers are 18 and 6.