The numerator of a fraction is 6 less than its denominator.

Step 1: Let the fraction be $x/y$, where numerator = $x$ and denominator = $y$.

Given: numerator is 6 less than denominator → $x = y - 6$

Step 2: After adding 2 to both, fraction = 2/3 → $(x+2)/(y+2) = 2/3$

Substitute $x = y - 6$ → $(y - 6 + 2)/(y + 2) = 2/3$ → $(y - 4)/(y + 2) = 2/3$

Step 3: Solve for $y$:

$3(y - 4) = 2(y + 2)$ → $3y - 12 = 2y + 4$ → $y = 16$

Step 4: Find $x$:

$x = y - 6 = 16 - 6 = 10$

Step 5: Simplest form:

Fraction = $x / y = 10 / 16 = 5 / 8$

Answer: 5/8