Question

Eliminate the parameter.

x = 4 cos t, y = 4 sin t

Answer 1

solve for t in x, then replace t by t(x) in y

Answer 2

Alternatively, you can take the fact that the parametric equations describe a circle with radius 4, so you have
\[(4\cos t)^2+(4\sin t)^2=4^2\\
x^2+y^2=16\]