1. The problem is to evaluate the expression $\frac{2}{3} \times \frac{82}{7}$.\n\n2. The formula for multiplying fractions is $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$.\n\n3. Applying the formula: $\frac{2}{3} \times \frac{82}{7} = \frac{2 \times 82}{3 \times 7}$.\n\n4. Calculate the numerator: $2 \times 82 = 164$.\n\n5. Calculate the denominator: $3 \times 7 = 21$.\n\n6. So, the product is $\frac{164}{21}$.\n\n7. This fraction cannot be simplified further because 164 and 21 have no common factors other than 1.\n\n8. Therefore, the final answer is $\frac{164}{21}$ or approximately 7.8095.