What is the product of one half of a number and one third of the same number?

The product of one half of a number ( x ) and one third of the same number ( x ) can be calculated by multiplying ( \frac{1}{2}x ) and ( \frac{1}{3}x ). This results in ( \frac{1}{2}x \times \frac{1}{3}x = \frac{1}{6}x^2 ). Therefore, the product is ( \frac{1}{6}x^2 ).