The correct spelling of the phrase "most obeying" is phonetically transcribed as /moʊst əˈbeɪɪŋ/. The word "most" is pronounced with a long O sound and the "t" at the end is silent. "Obeying" is pronounced with a short E sound, the "y" is pronounced as a long I, and the "ng" is pronounced as "ing". When written together, the word "obeying" changes to "obey" and adds the suffix "-ing" to indicate the present participle form of the verb.
The phrase most obeying does not have an etymology as it is not a standalone word. It appears to be a combination of the superlative adjective most and the present participle verb obeying. However, the word obey has an etymology of its own.
The word obey comes from the Old French word obeir, which originated from the Latin word oboedire. The Latin term was a combination of the prefix ob- (meaning toward or in the direction of) and the verb audire (meaning to hear). Obey originally carried the sense of to listen to or to hear and follow. Over time, the meaning evolved into its modern sense of to follow instructions or orders.