To find the x-intercepts of the function \( f(x) = 2(x - 6)(x - 6) \), we set the function equal to zero:
\[ f(x) = 0 \]
This means we need to solve:
\[ 2(x - 6)(x - 6) = 0 \]
Since \( 2 \) is a constant and does not affect the x-intercepts, we can simplify this to:
\[ (x - 6)(x - 6) = 0 \]
This simplifies to:
\[ (x - 6)^2 = 0 \]
The solution to this equation is:
\[ x - 6 = 0 \quad \Rightarrow \quad x = 6 \]
Since this factor is squared, the x-intercept at \( x = 6 \) has a multiplicity of 2. Thus, there is one unique x-intercept at \( x = 6 \).
In conclusion, the function \( f(x) = 2(x - 6)(x - 6) \) has one x-intercept.