To determine the probability that the basketball player will make six free throws out of the eight attempts, we refer to the provided probability distribution.
From the distribution table:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline
\text{Number of Free Throws Made} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
\text{Probability} & 0.002 & 0.008 & 0.004 & 0.12 & 0.23 & 0.20 & 0.11 & 0.00 & 0.02 \\
\hline
\end{tabular}
\][/tex]
Given the table, we can see that the probability of making exactly six free throws ([tex]\(X = 6\)[/tex]) is [tex]\(0.11\)[/tex].
Thus, the probability that the basketball player will make six free throws out of the eight attempts is:
[tex]\[
\boxed{0.11}
\][/tex]
