To solve the equation \(3(x - 6) = 60 - 10x\), follow these steps:

1. Distribute the 3 on the left side:
\[
3x - 18 = 60 - 10x
\]

2. Add \(10x\) to both sides to get all \(x\) terms on one side:
\[
3x + 10x - 18 = 60
\]
\[
13x - 18 = 60
\]

3. Add 18 to both sides to isolate the \(x\) term:
\[
13x - 18 + 18 = 60 + 18
\]
\[
13x = 78
\]

4. Divide both sides by 13 to solve for \(x\):
\[
x = \frac{78}{13}
\]
\[
x = 6
\]

So, the solution to the equation \(3(x - 6) = 60 - 10x\) is \(x = 6\).