suggests
To gently offer an idea for someone to consider.
To suggest means to offer an idea, possibility, or recommendation without insisting on it. When your teacher suggests you try a different approach to solving a math problem, she's not commanding you to do it: she's proposing it as something worth considering. When a friend suggests going to the park after school, he's putting the idea forward for the group to think about.
The word carries a gentle quality. Suggesting is softer than demanding, ordering, or requiring. If your parents suggest you wear a jacket, they think it's a good idea but they're leaving the final choice to you. If they tell you to wear a jacket, that's different: you need to do it.
Suggest can also mean to hint at something or give a slight indication. When dark clouds suggest rain is coming, they're showing signs that point toward that possibility. When a detective finds evidence that suggests someone was at a crime scene, the clues point in that direction without proving it completely.
The noun form is suggestion: “Do you have any suggestions for our science project?” Notice that suggestions invite consideration and discussion rather than ending the conversation. When someone makes a suggestion, they're opening a door for others to walk through if they choose.