Answer
$3\text{ square units}$
Work Step by Step
First we determine the $x$ and $y$ intercepts of the line $2y+3x-6=0$:
$$\begin{align*}
2(0)+3x-6=0&\Rightarrow x=2\\
2y+3(0)-6=0&\Rightarrow y=3.
\end{align*}$$
The triangle has the vertices $O(0,0)$, $A(2,0)$ and $B(0,3)$. It is a right triangle. Its area is:
$$\dfrac{OA\cdot OB}{2}=\dfrac{2\cdot 3}{2}=3\text{ square units}$$
