If half of a number is equal to two-thirds of 60, find the number.

Let the unknown number be $x$.
According to the problem statement:

$$\frac{1}{2}x=\frac{2}{3}\times 60$$

Simplify the right-hand side of the equation:

$$\frac{2}{3}\times 60=2\times 20=40$$

Now substitute it back into the equation to solve for $x$:

$$\frac{1}{2}x=40$$

$$x=40\times 2=80$$

Thus, the number is $80$.