Apply Ceva's Theorem, I Don't Think

Geometry Level 4

Let there be a triangle $$ABC$$ with $$AD$$ being a line passing through $$A$$ intersecting $$BC$$ (not extended) at $$D$$ and $$BE$$ being the line passing through $$B$$ and intersecting $$AC$$ (not extended) at $$E$$ let the intersection of $$AD$$ and $$BE$$ be $$H$$.

If the area of $$\Delta AHE$$ be $$2$$, the area of $$\Delta AHB$$ be $$3$$ and the area of $$\Delta BHD$$ be $$4$$. Find the area of $$CDHE$$.

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