The locus of the points represented by $|z+3|-|z-3|=6$, where $z$ is a complex number, is ....

Let $z = x + iy$ with $x, y \in \mathbb{R}$. The equation $|z+3| - |z-3| = 6$ describes a set of points where the difference of distances to $F_1 = -3$ and $F_2 = 3$ is constant. This defines a hyperbola, but with $2a = 6$ and $2c = |F_1 - F_2| = 6$, $a = c = 3$ implies the hyperbola degenerates.

The condition $|z - F_1| - |z - F_2| = |F_1 - F_2|$ requires that $z$ lies on the x-axis with $F_2$ between $F_1$ and $z$, so $y=0$. Substituting $z = x$, the equation becomes $|x+3| - |x-3| = 6$.

For $x \geq 3$, $|x+3| - |x-3| = (x+3) - (x-3) = 6$, which holds.
For $x < 3$, this equality fails: from $-3 \leq x < 3$, $x+3 - (3-x) = 2x$; setting $2x = 6$ gives $x=3$, a contradiction; for $x < -3$, $-(x+3) + (x-3) = -6 \neq 6$.

The locus is the ray $x \geq 3$ on the x-axis, corresponding to option D.