有關gramma的問題

Useful Patterns :
to suggest something ; to suggest doing something ; to suggest that someone (should) do something
e.g. (1) Can you suggest a good hotel? (2) He suggested John for the job. (3) The figures suggest an improvement in environmental damage. (4) We have so much to do, I don't suggest going away. (5) Who suggested doing it this way? (6) I suggest putting the meeting off . (7) He suggested that we (should) come another day. (8) I suggest that you (should) investigate the case again.
The first sentence below is commonly used :
1. I suggest that she (should) do exercise everyday. (right)
2. I suggest her doing exercise everyday. (right)

First of all, it is grammar not gramma

"I suggest that she do exercise everyday" is wrong..
: "I suggest that she does exercise everyday"

but then i think you can use better sentences..

"I would suggest her to exercise everyday"
or
"My suggestion for her is to exercise everyday"

It sounds really weird when you say "I suggest her" and "I suggest her to do exercise" because exercise is already an action, you don't need to put "do"..putting "do" in front of exercise is kinda like Chinese translates to English, and it would be a bit wordy.

no,
I suggest her to do exercise everyday

never ~~ her doing

this is better
I suggest her to do more exercise

No, the correct answer should be " I suggest her doing exercise everyday."