Answer
Ellipse

Work Step by Step
Given: $16x^{2}+9y^{2}-36y=108$
By completing the square, we get
$16x^{2}+9(y^{2}-4y+4)=108+9(4)$
$16x^{2}+9(y-2)^{2}=144$
Divide by $144$.
$\frac{x^{2}}{9}+\frac{(y-2)^{2}}{16}=1$
which is the standard form of the equation of an Ellipse.
$\frac{(x-h)^{2}}{b^{2}}+\frac{(y-k)^{2}}{a^{2}}=1$
Here, $(h,k)=(0,2)$
