Question 29454
Let n be the required number. From the problem, you can write:

{{{(n-2)/(n+6) = 2/3}}} Multiply both sides by (n+6)
{{{n-2 = (2/3)(n+6)}}} Multiply both sides by 3.
{{{3(n-2) 2(n+6)}}} Expand.
{{{3n-6 = 2n+12}}} Subtract 2n from both sides.
{{{n-6 = 12}}} Add 6 to both sides.
{{{n = 18}}}

Check: 
{{{(18-2)/(18+6) = 16/24}}} Reduce this fraction to {{{2/3}}}