6. Write 10 pairwise distinct positive integers $a_{1}, a_{2}, \cdots, a_{10}$ in the form of the following chart, where the number pointed to by two arrows equals the sum of the two numbers at the starting points of these arrows. For example $\stackrel{a_{1} \rightarrow a_{2}}{a_{5}}$ indicates $a_{2}=$ $a_{1}+a_{5}$. Then, the smallest possible value of $a_{4}$ that satisfies the following chart is ( ).
(A) 10
(B) 20
(C) 30
(D) 40
6. (B).
\[
\begin{aligned}
a_{4} & =a_{3}+a_{7}=\left(a_{2}+a_{6}\right)+\left(a_{6}+a_{9}\right) \\
& =a_{2}+2 a_{6}+a_{9} \\
& =\left(a_{1}+a_{5}\right)+2\left(a_{5}+a_{8}\right)+\left(a_{8}+a_{10}\right) \\
& =a_{1}+3 a_{5}+3 a_{8}+a_{10} .
\end{aligned}
\]

To minimize \(a_{4}\), we can first consider the values of \(a_{5}\) and \(a_{8}\), and then consider the values of \(a_{1}\) and \(a_{10}\).
(1) First, the values of \(a_{5}\) and \(a_{8}\) should be as small as possible. By symmetry, let's take \(a_{5}=1\) and \(a_{8}=2\), then \(a_{6}=3\).
(2) Next, the values of \(a_{1}\) and \(a_{10}\) should be as small as possible. By quasi-symmetry, let's take \(a_{1}=4\) (similar reasoning can be applied to \(a_{10}=4\)), then \(a_{2}=5\), \(a_{3}=8\).
When \(a_{10}=6\), \(a_{9}=8\), which contradicts \(a_{3}=8\);
When \(a_{10}=7\), \(a_{9}=9\), then \(a_{7}=12\), thus \(a_{4}=20\). Therefore, the minimum possible value of \(a_{4}\) is 20.