What happens phonetically in "words that"?

Solution 1:

Briefly (because stuff like this happens whenever words meet up in speech,
which is to say in every sentence), the phonemics of words that
(occurring in a phrase, where words is stressed and that is unstressed)
is something like:

• /'wərdzðət/

The big problem is that long consonant cluster in the middle:

• /rdzð/

The /r/ just colors the preceding schwa vowel to [ɚ], so it can be ignored.
But the /dzð/ cluster starts with a dental stop and transitions into a postdental sibilant /z/,
and then an interdental fricative /ð/, all of which requires a lot of complicated lip
and tongue movement, with breath coordination.

So what happens in practice is that things get lost. Consonant clusters are regularly simplified;
sixths changes from canonical /sɪksθs/ to /sɪkss/, for instance.

In the case of words that, the final /ð/ usually drops, producing

• /'wərdzət/

which sounds like words it or words at, but is understood as words that at ordinary speech rates.