Simplify the following expression: 2(a - 3b) - 2(3a - b)

The given expression is $2(a - 3b) - 2(3a - b)$.
Distribute 2 into the first parenthesis: $2 \times a = 2a$ and $2 \times (-3b) = -6b$.
Distribute $-2$ into the second parenthesis: $-2 \times (3a) = -6a$ and $-2 \times (-b) = +2b$.
So the expression becomes:

The like terms are those with $a$ and those with $b$.
Combine the $a$ terms: $2a - 6a = (2 - 6)a = -4a$.
Combine the $b$ terms: $-6b + 2b = (-6 + 2)b = -4b$.

Combine the results from Step 2: