How do you find the area of the triangle given A= 50 degrees, b= 12, c=14?

As Emma Nora said, you need to calculate the height of the triangle, but you need to use the ${50}^{o}$ angle in the calculation.
If we make the side of length 14 horizontal, then the height of the triangle is $12 \sin {50}^{o}$ and the area is
$\left(\frac{1}{2}\right) b a s e \cdot h e i g h t = \left(\frac{1}{2}\right) 14 \cdot 12 \cdot \sin {50}^{o}$
$= 84 \cdot \sin {50}^{o}$