6. The number of positive roots of the equation $2 x-x^{2}=\frac{2}{x}$ is ( ).
(A) 0
(B) 1
(C) 2
(D) 3
6. A.

When $x>2$, the left side $=(2-x) x < 0$, the original equation has no solution;
When $x=2$, the left side $=0$, the right side $=1$, the equation has no solution.
When $0<x<2$, the left side $2x-x^2$ is a downward-opening parabola, and the right side $\frac{2}{x}$ is a decreasing function. Since the left side is positive and the right side is positive in this interval, and the left side is greater than the right side at $x=1$, and the right side is greater than the left side at $x=2$, there is no intersection, so the equation has no solution.
When $x<0$, the left side $2x-x^2$ is positive, and the right side $\frac{2}{x}$ is negative, so the equation has no solution.
In summary, the number of roots of the equation $2x - x^2 = \frac{2}{x}$ is 0.