6. As shown in Figure 2, circles $\odot O_{1}$ and $\odot O_{2}$ are externally separated, and their line of centers $O_{1} O_{2}$ intersects $\odot O_{1}$ at points $A$ and $B$, and intersects $\odot O_{2}$ at points $C$ and $D$. Circle $\odot O_{3}$ is internally tangent to $\odot O_{1}$ at point $B$, and circle $\odot O_{4}$ is internally tangent to $\odot O_{2}$ at point $C$. The external common tangent of $\odot O_{2}$ and $\odot O_{3}$ passes through point $A$, touching $\odot O_{3}$ at point $E$ and $\odot O_{2}$ at point $F$. The external common tangent of $\odot O_{1}$ and $\odot O_{4}$ passes through point $D$. If the radius of $\odot O_{3}$ is 1.2, then the radius of $\odot O_{4}$ is ( ).
(A) 1
(B) 1.2
(C) 1.5
(D) 0.9
6. B.

Let the radius of $\odot O_{i}(i=1,2,3,4)$ be $r_{i}, BC=m$.
Obviously, $\triangle A E O_{3} \sim \triangle A F O_{2}$.
Thus, $\frac{O_{3} E}{O_{2} F}=\frac{A O_{3}}{A O_{2}} \Rightarrow \frac{r_{3}}{r_{2}}=\frac{2 r_{1}-r_{3}}{2 r_{1}+m+r_{2}}$
$\Rightarrow r_{3}=\frac{2 r_{1} r_{2}}{2 r_{1}+m+2 r_{2}}$.
Similarly, $r_{4}=\frac{2 r_{1} r_{2}}{2 r_{1}+m+2 r_{2}}$.
Therefore, $r_{4}=r_{3}=1.2$.