To solve this expression, we can use the properties of operations and rules for multiplying and dividing.
First, we need to simplify the expression by performing the multiplication and division from left to right.
To multiply -2 by 1/5, we multiply the numerators (-2 × 1) to get -2 and multiply the denominators (5 × 1) to get 5. So, -2 × 1/5 = -2/5.
Next, we divide -2/5 by 2/3. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 2/3 is 3/2. So, -2/5 ÷ 2/3 = -2/5 × 3/2.
To multiply fractions, we multiply the numerators (-2 × 3) to get -6 and multiply the denominators (5 × 2) to get 10. So, -2/5 × 3/2 = -6/10.
Next, we multiply -6/10 by -5/6. Again, we multiply the numerators (-6 × -5) to get 30 and multiply the denominators (10 × 6) to get 60. So, -6/10 × -5/6 = 30/60.
Finally, we divide 30/60 by 3/4. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 3/4 is 4/3. So, 30/60 ÷ 3/4 = 30/60 × 4/3.
To simplify 30/60 × 4/3, we can reduce 30/60 to 1/2. So, 1/2 × 4/3 = 4/6.
To further simplify 4/6, we can divide the numerator and denominator by their greatest common factor, which is 2. So, 4/6 = 2/3.
Therefore, (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) = 2/3.