e) $\frac{1}{6} x \frac{2}{3}$

Step 1 ：The problem is asking for the product of two fractions, \(\frac{1}{6}\) and \(\frac{2}{3}\).

Step 2 ：To multiply fractions, we multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together.

Step 3 ：So, we need to multiply 1 and 2 for the numerator and 6 and 3 for the denominator.

Step 4 ：The product of the numerators is 2 and the product of the denominators is 18, so the product of the two fractions is \(\frac{2}{18}\).

Step 5 ：However, this fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

Step 6 ：After simplifying, the numerator is 1 and the denominator is 9.

Step 7 ：So, the simplified product of the two fractions is \(\boxed{\frac{1}{9}}\).