To calculate the value of 2/3 ÷ 4/5, we need to divide the numerator of the first fraction by the numerator of the second fraction and divide the denominator of the first fraction by the denominator of the second fraction.

2/3 ÷ 4/5 = (2/3) * (5/4) (dividing by a fraction is the same as multiplying by its reciprocal)

Now, we can multiply the numerators together and the denominators together:

(2/3) * (5/4) = (2 * 5) / (3 * 4) = 10/12

The fraction 10/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:

10/12 = (10 ÷ 2) / (12 ÷ 2) = 5/6

Therefore, the value of 2/3 ÷ 4/5 is 5/6.