cosmology - How far has a 13.7 billion year old photon travelled

I've read that the size of the observable Universe is thought to be around ~46 billion light years, and that the light we see from the most distant galaxies were emitted ~13.7 billion years ago as a result of the expansion. So is the actual distance the photons have travelled 46 billion light years, or 13.7 billion light years?

Answer

Age of universe is roughly 13.8 billion years, so anything with longest traveling record can only travel 13.8 billion light years at most (in any direction; not necessarily to Earth) because nothing can travel faster than light.

Now, we are at the center of the observable universe (which is spherical with visible radius 13.8 billion years), so longest traveling record holders are the oldest ones and are at the edge of the observable universe and they have traveled 13.8 billion light years so far.

The actual calculated radius 46 billion light years is different from the visible radius because the universe has expanded.

So, the answer to your question is 13.8 billion light years.