Why is 挺 used in the following sentence?
太 is usually a compound with 了. So if 太 was the correct answer it would be: ___精神了。

好 would work in dialect/topolect in place of 很 - but is incorrect in MSM.

多么 is just weird. maybe it work work with 啊 like ___精神啊 - but now were moving away from MSM again.

挺 is pretty much interchangeable with 很


Spiritual is not the correct translation here for 精神.
MDBG defines it as:

精神
jīng​shen​
vigor / vitality / drive / spiritual

红光满面，挺精神的。
glowing with health - looking full of vigor (energetic/lively/spirited)