The common-sense definitions relating distance to velocity and time are approximations that hold over cosmically short distances, for which the expansion of space can be approximated to be zero.
Space expands, increasing not only the distance between the emitter and the detector, but also the distance the light must travel on the way from the emitter to the detector. Supposing that the relative velocity between our galaxy and some distant galaxy was 0 13.6 GY ago, the light emitted from that galaxy was emitted when our galaxy was much, much closer than 13.6 GLY away, and that galaxy is now much, much farther than 13.6 GLY away. The distance traveled by the light itself, called the lookback distance, is 13.6 GLY. Astronomers seem to have a habit of using lookback distance when communicating to the public, which avoids confusion in some regards but causes confusion in other regards. In technical publications, I have seen redshift factor ($z$) as a metric of cosmic distances.
Imagine an ant walking along a strip of (very!) stretchy rubber material. He starts out 10cm away from a speck of sugar and walks towards it at 1 cm/s. We mark the place where he starts. However, we stretch the rubber strip at such a rate that for every 1cm of distance, the length of the rubber increases at a rate of 0.2 cm/s. The longer the distance, the more it stretches in a given period of time. The ant keeps walking and walking, but he only ever gets farther from the the sugar. After 3 seconds, the ant has traveled 3 centimeters, the distance between the starting mark and the sugar is about 18cm, the distance from the ant to the sugar is about 14cm, and the distance from the ant to the starting mark is about 4 cm.
Here the ant represents light moving from fairly nearby objects in the early universe, when the rate of expansion (that is: how much stretch per unit distance) was much higher than it is now.
Suppose that as time goes on, the stretching rate of the strip gets gradually smaller and smaller. If the ant started out close enough, and the stretching rate gets small enough, even though he may be hundreds of centimeters from the sugar by time it happens, there may eventually come a time when the ant's steady 1 cm/s march across the stretchy rubber exceeds the stretching speed. If it does, even by a tiny bit, it will eventually reach the sugar, because as the ant keeps going, and the distance to the sugar gets less, the amount that the distance to the sugar stretches per second will also get less. But all the while, the distance to the starting mark will keep increasing.
Here the ant represents light that was emitted in the early universe from a cosmically close distance, traveled for 13+ billion years from a starting point that is now 30+ billion light years away from us, and has finally reached the detector.