Answer
An infinitely long circular cylinder with radius 4 centered at the x-axis.
Work Step by Step
The given equation does not include $x$, so $x$ can take on every possible value. This means that the region will extend infinitely along the x-axis. At any fixed value of $x$, say $x = k$, we recognize $y^{2} + z^{2} = 16$ to be a circle k units in front of the yz-plane, with radius 4 and center (k, 0, 0). Therefore, our region will be made up of infinite copies of this circle, one for every value of x. This makes an infinitely long circular cylinder with radius 4 and the x-axis as its central axis.
