A line \( l \) with slope \(-2\) intersects the positive \(x\)-axis at \(A\) and the positive \(y\)-axis at \(B\). Another line \( m \) intersects the \(x\)-axis at \(C(6,0)\) and the \(y\)-axis at \(D\). The lines \( l \) and \( m \) intersect at \(E(2,2)\). What is the area of triangle \( \triangle OEC \)? Let's think step by step and output the final answer within \boxed{}.
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