Answer: 3

Write $f(x) = mx + 6$. Then $f(4) = 4m + 6$ and $f(1) = m + 6$. The condition $f(4) = 2f(1)$ gives $4m + 6 = 2(m + 6) = 2m + 12$. So $2m = 6$ and $m = 3$.

Writing $2f(1)$ as $2m + 6$ instead of $2(m + 6)$ gives $m = 0$.