Nancy bought 15m of ribbon.
Her sister bought 15-6 = 7m or ribbon.
Let x and y be the price of Nancy and her sister's ribbon respectively.
Given,
15x + 7y = 6 ----(1)
also
y = 2x -----------(2)
Now putting the value of y of eq(2) in eq(1) we get,
15x + 7(2x) = 600
=> 15x + 14x = 600
=> x = 6/29
Also, y = 2x = 2 * 600/29 = 1200/29
So the price of Nancy's ribbon per metre = 600/29
and price of her sister's ribbon pre metre = 1200/29
In my country 6,00 is equal to 600 and not 6. So I don't know which one you want. If you want the latter then
your x will be 6/29, and y will be 12/29