Evaluate the value of $ - \dfrac{4}{7} - \dfrac{2}{{ - 3}}$ .

Hint: Here, we are asked to find the value of $ - \dfrac{4}{7} - \dfrac{2}{{ - 3}}$ .
Firstly, simplify the given question by removing the negative sign of the denominator.
Then, take the LCM of the two denominators.
Thus, find the value of the required answer.

Complete step-by-step answer:
Here, we are asked to find the value of $ - \dfrac{4}{7} - \dfrac{2}{{ - 3}}$ .
We will firstly simplify the given question as
 $
   - \dfrac{4}{7} - \dfrac{2}{{ - 3}} \times \dfrac{{ - 1}}{{ - 1}} \\
   = - \dfrac{4}{7} - \left( { - \dfrac{2}{3}} \right) \\
   = - \dfrac{4}{7} + \dfrac{2}{3} \\
   = \dfrac{2}{3} - \dfrac{4}{7} \\
 $
Now, we will solve the value of $\dfrac{2}{3} - \dfrac{4}{7}$ .
To do so, we need to find the LCM of 7 and 3.
The numbers 7 and 3 will give the LCM as $7 \times 3 = 21$ .

 $\therefore \dfrac{2}{3} - \dfrac{4}{7} = \left( {\dfrac{2}{3} \times \dfrac{7}{7}} \right) - \left( {\dfrac{4}{7} \times \dfrac{3}{3}} \right)$
 $
   = \dfrac{{14}}{{21}} - \dfrac{{12}}{{21}} \\
   = \dfrac{{14 - 12}}{{21}} \\
   = \dfrac{2}{{21}} \\
 $
Thus, we get the value of $ - \dfrac{4}{7} - \dfrac{2}{{ - 3}}$ as $\dfrac{2}{{21}}$ .

Note: LCM of numbers:
Least Common Multiple (LCM) of any two numbers, say x and y, is the smallest positive integer that is divisible by both x and y. It is usually denoted by \[LCM\left( {x,y} \right)\] .
For example, the given two numbers are 3 and 5. So, the LCM of the numbers 3 and 5 will be $3 \times 5 = 15$. Thus, LCM of the numbers 3 and 5 is 15, which is divisible by both 3 and 5.