To solve the equation \( 4 (c - 2) = 2 (5 - c) \), we will first distribute both sides of the equation.
Starting with the left side: \[ 4(c - 2) = 4c - 8 \]
Now for the right side: \[ 2(5 - c) = 10 - 2c \]
Now we can rewrite the equation with these expressions: \[ 4c - 8 = 10 - 2c \]
Next, we will add \( 2c \) to both sides to get all the \( c \) terms on one side: \[ 4c + 2c - 8 = 10 \] \[ 6c - 8 = 10 \]
Now, add \( 8 \) to both sides: \[ 6c = 10 + 8 \] \[ 6c = 18 \]
Now, divide both sides by \( 6 \): \[ c = \frac{18}{6} \] \[ c = 3 \]
So, the solution to the equation is: \[ \boxed{3} \]