Find the value and express as a rational number in standard form:
$-6\div \left( \dfrac{-8}{17} \right)$

Hint: First, we should know the formula to calculate the diving of the two rational numbers. Then, we know that for dividing two rational numbers, firstly we must reciprocate the second rational number and then multiply it with the first one. Then, we know another fact that multiplication of the two negative numbers gives the positive number. Then, just by simplifying solving them by multiplying 17 to 6 and then dividing the result with 8, we get our final result.

Complete step-by-step answer:
In this question, we are supposed to find the value of the question given by using basic mathematics of the dividing of the rational numbers.
So, we should know the formula to calculate the diving of the two rational numbers as:
$-6\div \left( \dfrac{-8}{17} \right)$
Now, we know that for dividing two rational numbers, firstly we must reciprocate the second rational number and then multiply it with the first one.
So, first find the reciprocal of the second rational number as:
$\dfrac{-17}{8}$
Now, multiplying with the first rational number which is $-8$.
So, writing the both the above steps in single line as:
$-6\div \left( \dfrac{-8}{17} \right)=-6\times \left( \dfrac{-17}{8} \right)$
Now, we know another fact that multiplication of the two negative numbers gives the positive number.
So, by applying this method, we get the solution of above expression as:
$-6\times \left( \dfrac{-17}{8} \right)=6\times \dfrac{17}{8}$
Now, just by simplify solving them by multiplying 17 to 6 and then dividing the result with 8 as:
$\begin{align}
  & 6\times \dfrac{17}{8}=\dfrac{102}{8} \\
 & \Rightarrow \dfrac{51}{4} \\
\end{align}$
So, it gives the final value of the expression as $\dfrac{51}{4}$.
Hence, $\dfrac{51}{4}$ is the final answer.

Note: The only mistake we can make in this type of the question is that we reciprocate the first term of the equation and then multiply it with the second rational number which is wrong and we get the wrong answer. So, if we do that we get the following answer as:
$\dfrac{-1}{6}\times \dfrac{-8}{17}=\dfrac{4}{51}$
which is a wrong answer and its reciprocal of the final answer.