How do you solve $\left[ {12 - 3 + 4m - 6\left( {3m - 2} \right)} \right] = - 7\left( {2m - 8} \right) - 3\left( {m - 2} \right) + 3m - 5$?

Hint: In this question we have to solve the equation for $m$, for this we will open the brackets and then simplifying the given equation, then the equation will become a linear equation with the degree of the highest exponent of $m$ is equal to 1. To solve the equation take all $m$ terms to one side and all constants to the others side and solve for the required $m$.

Complete step by step solution:
Given equation is $\left[ {12 - 3 + 4m - 6\left( {3m - 2} \right)} \right] = - 7\left( {2m - 8} \right) - 3\left( {m - 2} \right) + 3m - 5$, and we have to solve for $m$,
Now transform the given equation by opening the brackets, i.e.,
$ \Rightarrow 12 - 3 + 4m - 18m + 12 = - 14m + 56 - 3m + 6 + 3m - 5$,
Now simplifying the equation by eliminating the like terms we get,
$ \Rightarrow 9 - 14m + 12 = - 14m$,
Now simplifying the equation we get,
$ \Rightarrow 21 - 14m = - 14m$,
Now we got an equation which is a linear equation as the highest degree of $x$ will be equal to 1,
Now subtract 21 to both sides of the equation, we get,
$ \Rightarrow 21 - 14m - 21 = - 14m - 21$,
Now simplifying we get,
$ \Rightarrow - 14m = - 14m - 21$,
Now add 14m to both sides we get,
$ \Rightarrow - 14m + 14m = - 14m - 21 + 14m$,
Now simplifying we get,
$ \Rightarrow 0 = - 21$, which is not possible,
Therefore the above statement is not true, so there are no real solutions for the given equation.

$\therefore $ The value of $m$ when the equation $\left[ {12 - 3 + 4m - 6\left( {3m - 2} \right)} \right] = - 7\left( {2m - 8} \right) - 3\left( {m - 2} \right) + 3m - 5$ will have no real solutions.

Note: A linear equation is an equation of a straight line having a maximum of one variable. The degree of the variable will be equal to 1. To solve any equation in one variable, pit all the variable terms on the left hand side and all the numerical values on the right hand side to make the calculation solved easily.