Simplify the expression below. \( \left(\frac{2 n}{6 n+4}\right)\left(\frac{3 n+2}{3 n-2}\right) \) What is the numerator of the simplified expression?

To simplify the expression \( \left(\frac{2 n}{6 n+4}\right)\left(\frac{3 n+2}{3 n-2}\right) \), we first simplify the individual fractions. Starting with the denominator of the first fraction: \[ 6n + 4 = 2(3n + 2) \] So, we can rewrite the first fraction: \[ \frac{2n}{6n + 4} = \frac{2n}{2(3n + 2)} = \frac{n}{3n + 2} \] Now, substituting this into the original expression gives: \[ \left(\frac{n}{3n + 2}\right)\left(\frac{3n + 2}{3n - 2}\right) \] Multiplying these fractions, we find: \[ \frac{n(3n + 2)}{(3n + 2)(3n - 2)} \] The \(3n + 2\) cancels out: \[ \frac{n}{3n - 2} \] Thus, the simplified expression is: \[ \frac{n}{3n - 2} \] The numerator of the simplified expression is: \[ \boxed{n} \]