OA: 2x+y=0OA//BC$\Rightarrow$BC:2x+y+m=0(m$\neq$0)
B=d1$\cap$BC$\Rightarrow$B(1-m;m-2)
C=d2$\cap$BC$\Rightarrow$C(m-2;4-3m)
S OABC=$\frac{1}{2}$(OA+BC).d(O,BC)
$\Leftrightarrow$$\frac{1}{2}$.$\left[ {\sqrt{(-1)^{2}+2^{2}}+\sqrt{(2m-3)^{2}+(4m-6)^{2}}} \right]$.$\frac{\left| {m} \right|}{\sqrt{2^{2}+1}}$=6
$\Leftrightarrow$($\left| {2m-3} \right|$+1).$\left| {m} \right|$=12
$\Leftrightarrow$m=1 - $\sqrt{7}$ or m=3
$\Rightarrow$B($\sqrt{7}$;-1-$\sqrt{7}$)&C(-1-$\sqrt{7}$;1+3$\sqrt{7}$)
or B(-2;1)&C(1;-5)