Simplify the following expression: 4/5 * 2/3 - 2/10 / 3/5

To divide by a fraction, multiply by its reciprocal.

$$\frac{2}{10} \div \frac{3}{5} = \frac{2}{10} \times \frac{5}{3}$$

Multiply the numerators and the denominators.

$$\frac{2 \times 5}{10 \times 3} = \frac{10}{30}$$

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 10.

$$\frac{10 \div 10}{30 \div 10} = \frac{1}{3}$$

$$\frac{8}{15} - \frac{1}{3}$$

To subtract these fractions, find a common denominator. The least common multiple of 15 and 3 is 15.
Convert $\frac{1}{3}$ to an equivalent fraction with a denominator of 15.

$$\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}$$

Now perform the subtraction.

$$\frac{8}{15} - \frac{5}{15} = \frac{8 - 5}{15} = \frac{3}{15}$$

Divide the numerator and denominator by their greatest common divisor, which is 3.

$$\frac{3 \div 3}{15 \div 3} = \frac{1}{5}$$

The simplified expression is $\frac{1}{5}$.