Final answer:
The correct final stable syllable to add to 'admis' is 'sion', resulting in the word 'admission'.
Step-by-step explanation:
The final stable syllable that should be added to the word "admis" is "sion", which yields the word "admission". This follows the provided pattern where palatalization occurs, usually changing a spelling to represent the [ch] sound. As ion is the suffix, it behaves according to this pattern when it is added to a base word ending in -t or -s. Additionally, "sion" is a common suffix that follows the consonant d in English words to create nouns, particularly from verbs. The suffix "-tion" could be an alternative, but it is not available in the given options. The other options provided, "sian" and "siont" are not commonly used or grammatically correct endings for the base provided.