How do you solve $ 4(c - 3) = 4c + 8? $

Hint: In this solution first of all we will open the bracket on the left hand side of the equation and then will move all the terms on the left hand side of the equation. Then simplify the equation finding the like terms.

Complete step by step solution:
Take the given expression: $ 4(c - 3) = 4c + 8 $
Multiply the term and open the bracket on the left hand side of the equation.
 $ 4c - 12 = 4c + 8 $
Move all the terms on the left hand side of the equation from the right hand side of the equation. When you move any term from one side to another then the sign of the term also changes. Positive terms become negative and the negative term becomes positive.
 $ \Rightarrow 4c - 12 - 4c - 8 = 0 $
Arrange like terms together.
 $ \Rightarrow \underline {4c - 4c} - \underline {12 - 8} = 0 $
Like terms with equal value and the opposite sign cancel each other, simplify the above equation.
 $ \Rightarrow - 12 - 8 = 0 $
When you simplify between two negative terms you have to do addition and give minus sign to the resultant value.
 $ \Rightarrow - 20 = 0 $
Above equation is not possible
But in actual $ - 20 \ne 0 $ and so the given equation has no solution.

Note: Always remember that like terms with the same value and opposite sign cancel each other. Remember following rules While doing simplification -
Addition of two positive terms gives the positive term
Addition of one negative and positive term, you have to do subtraction and give sign of bigger numbers, whether positive or negative.
Addition of two negative numbers gives a negative number but in actual you have to add both the numbers and give a negative sign to the resultant answer.