The answer is actually a bit complicated. To define the "speed" of anything, you really need a spacetime coordinate system that can assign position and time coordinates to different points in spacetime, so you can pick two points which lie on the moving object's path and calculate (difference in position coordinate)/(difference in time coordinate) and call that the speed. As it turns out, when physicists say that the speed of light has a constant value (labeled 'c' and equal to 299792458 meters/second), and that massive objects must always travel slower than c, they are only talking about its speed in
inertial frames, a set of non-accelerating coordinate systems which play an important role in relativity. In non-inertial coordinate systems this rule no longer applies, massive objects can have a coordinate speed greater than c, and light itself can have a coordinate speed different than c. "Inertial frames" are used in Einstein's theory of "special relativity" where gravity is ignored, but in Einstein's theory of "general relativity" where gravity causes spacetime to become "curved" (see
here for some discussion on both versions of relativity), it turns out that no coordinate systems covering large regions of curved spacetime actually qualify as "inertial", but if you zoom in on an arbitrarily small region of curved spacetime the effects of curvature become negligible (similar to how if you zoom in on a small region of a curved surface like the Earth, it looks approximately flat), and so one can define "local" inertial frames in any small region, which according to the
equivalence principle will be the local rest frames of observers in free-fall (if you're in free-fall you don't feel the effects of gravity). So in the local neighborhood of an observer free-falling into a black hole, light still moves at c and nothing can move faster c (and if that observer is crossing the event horizon, the horizon seems to be moving outward at c), but in some arbitrary non-inertial coordinate system covering a large region of spacetime both inside and outside the black hole these rules won't necessarily apply (and in general relativity the choice of how to define coordinate systems really is totally arbitrary, see the discussion of 'diffeomorphism invariance'
here), not even
outside the event horizon (although there is a special type of coordinate system known as
Kruskal-Szekeres coordinates where they do). Something similar is true in cosmology, where according to the usual notion of "distance" and "time" used in an expanding universe, galaxies sufficiently far away from us may be moving away with a "speed" greater than c, and light itself may have a "speed" different than c (see the third paragraph
here for a discussion), but any freefalling observer in the neighborhood of one of those distant galaxies would measure all massive objects in their local neighborhood moving slower than c and would measure light to still move at c.
