To solve the equation \([(7x - 63) / 3 - 105] \cdot 6 = 840\), let's break it down step by step.

1. First, simplify the expression inside the brackets:
\[
(7x - 63) / 3 - 105
\]

2. Distribute the division inside the brackets:
\[
\frac{7x - 63}{3} - 105
\]

3. Simplify \(\frac{7x - 63}{3}\):
\[
\frac{7x}{3} - \frac{63}{3} = \frac{7x}{3} - 21
\]

4. Substitute this back into the equation:
\[
\left(\frac{7x}{3} - 21 - 105\right) \cdot 6 = 840
\]

5. Combine the constants inside the brackets:
\[
\frac{7x}{3} - 126
\]

6. Now, multiply the entire expression by 6:
\[
\left(\frac{7x}{3} - 126\right) \cdot 6 = 840
\]

7. Distribute the 6:
\[
6 \cdot \frac{7x}{3} - 6 \cdot 126 = 840
\]

8. Simplify the multiplication:
\[
2 \cdot 7x - 756 = 840
\]
\[
14x - 756 = 840
\]

9. Add 756 to both sides to isolate the term with \(x\):
\[
14x = 1596
\]

10. Divide both sides by 14 to solve for \(x\):
\[
x = \frac{1596}{14}
\]
\[
x = 114
\]

So, the solution to the equation is:
\[
x = 114
\]