6. A line $l$ is drawn through point $P(2,1)$, intersecting the two coordinate axes at points $A$ and $B$. When the area $S$ of $\triangle A O B$ takes values in $(0,+\infty)$, the number of lines $l$ that can be drawn is ( ) lines.
(A) 2
(B) 3
(C) 2 or 3
(D) 2 or 3 or 4
6.D.

The line $l$ passes through $P(2,1)$ and forms a triangle with the two coordinate axes in the first quadrant, the minimum area of which is 4. In fact, let the equation of $l$ be
$$
\frac{x}{a}+\frac{y}{b}=1(a>0, b>0),
$$

then $\frac{2}{a}+\frac{1}{b}=1 \geqslant 2 \sqrt{\frac{2}{a} \cdot \frac{1}{b}}, a b \geqslant 8$.
Thus, $S=\frac{1}{2} a b \geqslant 4$.
When $S=4$, there are 4 lines.