About 130 miles?
No Chris, a lot more than that. You'll get that result from entering "Walking" into most map sites, but I won't be cycling directly over the mountains of central Wales on little tracks.
The route actually works out at >180.
We're both wrong.
139 miles to Carmarthen. (Including short detour to Bethlehem)
Exactly 160 miles home.
So, 21 miles to travel 15 from Carmarthen.