8. Given positive real numbers $a, b, c$ satisfy $2(a+b)=a b$, and $a+b+c=a b c$, then the maximum value of $c$ is

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$$
a+b+c=\frac{1}{2} a b+c=a b c \Rightarrow c=\frac{\frac{1}{2} a b}{a b-1}=\frac{1}{2} \cdot \frac{1}{1-\frac{1}{a b}} \text {, and } 2(a+b)=a b \geqslant 4 \sqrt{a b} \Rightarrow a b \geqslant 16 \text {, }
$$

equality holds when $a=b=4$, thus $c \leqslant \frac{8}{15}$. Therefore, the maximum value of $c$ is $\frac{8}{15}$.