The phrase "that under" is spelled using the following IPA symbols: /ðæt/ /ˈʌndər/. "That" is pronounced with a voiced dental fricative /ð/ sound and the short vowel sound /æ/. "Under" is pronounced with a primary stress on the first syllable and a schwa sound /ə/ on the second syllable. The /n/ and /d/ sounds are pronounced separately, with the final syllable ending in an /r/ sound. This spelling accurately reflects the pronunciation of the phrase.
The phrase "that under" does not have a distinct etymology because it is not a commonly used phrase or a well-known idiom. However, if you are referring to the separate words "that" and "under", they have their own etymologies.
The word "that" originated from the Old English word "þæt" in the 7th century, and it is related to other Germanic languages such as Old Frisian "thet" and Old High German "daz". It ultimately derives from the Proto-Germanic demonstrative pronoun "þat" meaning "that".
The word "under" has a longer history, dating back to Old English as well. It can be traced to the Proto-Germanic root word "*undar" or "*undraz".