Subtract $6a - 3b$ from $ - 8a + 9b$.

Hint: According to the question given in the question we have to subtract $6a - 3b$ from $ - 8a + 9b$. So, in the question there are two linear equations with two variables a and b. We know that if a variable is given in x that it can be added and subtracted with the same variable x to obtain the result.
As we know that when a negative number/term or variable is added with the negative number/term or variable then the result will be the addition of both of the number/term or variable but the sign will be negative but if a negative number/term or variable is added with the positive number/term or variable then the result will be the subtraction of both of the number/term or variable but the sign will be depend on the greater number.
And when we multiply a negative number/term or variable with the other negative number/term or variable the multiplication obtained will be positive and when we multiply a negative number/term or variable with the other positive number/term or variable the multiplication obtained will be negative.

Complete step-by-step answer:
Step 1: As given in the question we have to subtract $6a - 3b$ from $ - 8a + 9b$
Hence,
$ = -8a + 9b - ( 6a - 3b)$
Step 2: Now, on solving the obtained expression in step 1 and as we know that when we multiply a negative number/term or variable with the other negative number/term or variable the multiplication obtained will be positive and when we multiply a negative number/term or variable with the other positive number/term or variable the multiplication obtained will be negative as mentioned in the solution hint.
$ = - 6a + 3b - 8a + 9b$
$ = - 14a + 12b$
Step 3: Now, taking 2 as a common term from the expression obtained in step 2.
$ = 2(-7a + 6b)$

Hence, the subtraction of $6a - 3b$ from $ - 8a + 9b$ is $ = 2(-7a + 6b)$

Note: A negative term is added with the negative term then the result will be the addition of both of the terms but the sign will be negative but if a negative term is added with the positive term then the result will be the subtraction of both of the terms but the sign will be dependent on the greater number.
A negative term is multiplied with the other negative term the multiplication obtained will be positive and when we multiply a negative term with the other term or variable the multiplication obtained will be negative.