Can I host my website on shared hosting?

Usually, yes. The question is whether you want to.
If you are launching a more-or-less basic site which will have limited traffic — such as a personal blog, a homepage for a small offline business, or a website for local non-profit organizations — then shared hosting is a great way to go. It will provide all the hosting power you need for up to several hundred visitors a day, for a reasonably low cost.
If you need a website that will work with larger traffic numbers — several thousand a day, especially highly engaged visitors on an interactive site (like a store or web app) — then shared hosting is going to be a terrible experience for you. You would be better off, in that case, with a VPS hosting plan.