Answer
Ellipse shifted 4 units left and 2 units down.
Work Step by Step
$\frac{(x+4)^2}{9}+\frac{(y+2)^2}{16}=1$
The first aspect to notice is both the x term and y term are squared. The second aspect to notice is the two squared terms are both positive but both are divided by unequal numbers (9 and 16). This means the conic is an ellipse. The $(x+4)$ means that the center is shifted four units left (along the x-axis). The $(y+2)$ means that the center is shifted two units down (the y-axis).
