Is there any word in English where "th" sounds like "t+h"?

Solution 1:

In general, the "t" and "h" in "th" are only pronounced on their own when they appear in English words that originated as compound words (such as rat-hole becoming "rathole", foot-hill becoming "foothill", and light-house becoming "lighthouse"). In each of these cases "th" is not a single sound, but rather two sounds, "t" and "h".

Instead, "th" is almost universally (in English, that is) used as a digraph (which means that both the 't' and the 'h' combine to form a single sound; in other words, you could replace the "th" with some symbol without losing meaning). Basically, if you wanted to, you could consider "th" its own letter.

The primary ways "th" is used in English are:
As a voiceless dental fricative, such as in "thing", "thug", "throw", or "math".
As a voiced dental fricative, such as in "this", "then", "soothe", "lithe", "bathe", or "smooth" (which a long time ago used to be spelled "smoothe").

While those are the primary uses of "th", there are some instances where "th" is used to import foreign words, that have sounds that most English speakers can't differentiate/can't pronounce (for example, I think the word "Thailand" is written with a "Th" because the "t" sound is supposed to be an aspirated consonant, but I can't make or understand the difference between that and non-aspirated sounds, so I'm not the best judge for that); typically we'll take those sounds and ignore aspiration, or pronounce them in one of the other two ways I mentioned.

It may also interest you to look at the letter thorn Þ, which was used in written English several-hundred years ago. It was replaced by "th" as German printing presses did not come with the symbol, and adding it in would have been too costly.

Solution 2:

Words such as rathole, carthorse and pithead are pronounced rat hole, cart horse and pit head.