The phrase "suggest sb to do" is correct, and "suggest sb doing" is also correct, but they have slightly different meanings and usage contexts.
✅ "Suggest sb to do"
This is the correct and common form when you want to recommend or advise someone to do something.
Example:
- She suggests to go to the park.
- He suggests to study more hard.
✅ "Suggest sb doing"
This is also correct, but it's used when you're saying that something is happening or is being done, not that you're advocating or advising someone to do it.
Example:
- The teacher suggests that we do the assignment.
- The weather suggests that it will rain.