To find the x-intercept of the line given by the equation \( y = \frac{3}{10}x - 6 \), we set \( y \) to 0 and solve for \( x \).
Starting with the equation:
\[ 0 = \frac{3}{10}x - 6 \]
Next, we add 6 to both sides:
\[ 6 = \frac{3}{10}x \]
Now, to isolate \( x \), we can multiply both sides by the reciprocal of \( \frac{3}{10} \), which is \( \frac{10}{3} \):
\[ x = 6 \cdot \frac{10}{3} \]
Calculating the right side:
\[ x = \frac{60}{3} = 20 \]
Thus, the x-intercept of the line is \( \boxed{20} \).