Evaluate the numerator.

The numerator is $\frac{6}{7} \text{ of } 14 \div 80 \times -20$.
First, calculate "$\frac{6}{7}$ of 14":

$$\frac{6}{7} \times 14 = 6 \times \frac{14}{7} = 6 \times 2 = 12$$

Now substitute this back into the numerator:

$$12 \div 80 \times -20$$

Perform division and multiplication from left to right:

$$\frac{12}{80} \times -20 = \frac{3}{20} \times -20 = -3$$

So, the numerator is $-3$.

The denominator is $-2 \times 5 + (14 \div 7) \times 3$.
First, calculate the expression in parentheses:

$$14 \div 7 = 2$$

Substitute this back into the denominator:

$$-2 \times 5 + 2 \times 3$$

Perform multiplications from left to right:

$$(-2 \times 5) + (2 \times 3) = -10 + 6$$

Now perform the addition:

$$-10 + 6 = -4$$

So, the denominator is $-4$.

$$\frac{-3}{-4} = \frac{3}{4}$$

The final answer is $\frac{3}{4}$.