Find the intercepts.
[tex]2x+3y=12 \\ \\
\hbox{x-intercept - y=0}: \\
2x+3 \times 0=12 \\
2x=12 \\
x=\frac{12}{2} \\
x=6 \\ \\
\hbox{y-intercept - x=0} : \\
2 \times 0 +3y=12 \\
3y=12 \\
y=\frac{12}{3} \\
y=4[/tex]
Look at the picture.
[tex]A=\frac{6 \times 4}{2}=\frac{24}{2}=12[/tex]
The area is 12 square units.
