1 to say that you are willing to give someone something, or to hold something out to them so that they can take it : offer sb sth: You haven't offered Grandma any ice cream. | They offered him a very good job but he turned it down. | offer sth to sb: Offer some coffee to the guests.
2 to say that you are willing to pay a particular amount of money : offer (sb) sth for: They've offered us £75,000 for the house. | The police are offering a reward for any information.
3 to say that you are willing to do something: I don't need any help, but it was nice of you to offer. | offer to do sth: My dad has offered to pick us up. | Shelly didn't even offer to help.
4 to provide something that people need or want: He offered no explanation for his actions. | offer sth to sb: Senator Joseph's speech will have offered little comfort to bankrupt businessmen. | have sth to offer (to sb): Edinburgh has a great deal to offer to visitors in the way of entertainment.
5 offer (up) a prayer/sacrifice etc to pray to God or give something to God
6 offer itself formal if an opportunity offers itself, it happens for you: I shall be ready to raise the matter with him when a suitable occasion offers itself.
7 offer your hand to sb to hold out your hand in order to shake hands with someone
suggest
1 to tell someone your ideas about what they should do, where they should go etc: If this is not convenient, please suggest another date. | suggest doing sth: John suggested going together in one car. | suggest (that): She suggested that we write that into the contract. | can/may I suggest (=used to politely suggest a different idea): May I suggest that you see a financial advisor? | suggest how/where etc: Can you suggest where to stay in Rio?
2 to tell someone about a suitable person for a job : suggest sb for: Mr Roberts Guarino has been suggested for the post of director.
3 to make someone think that a particular thing is true; indicate (1): The actual number of rapes may be higher