Here's a link that will give you some options:
You can recover facebook password. You need to recovery Email or your phone number.
If you have no recovery Email then you can recover using this method.
There're a few solutions to reset your password and get your account back under different circumstance.
If you can still remember your old password, this support page might help you:
If you don't remember the password and even forgot your email/phone number when registered, you might need to try the methods below and see if one of them works.
1. Try logging in with an alternate email or phone number
You may be able to get back into your Facebook account by using an alternate email or mobile phone number listed on your account.
If you don't know what alternate information you have:
- Go to facebook.com/login/identify and follow the instructions.
- Make sure to use a computer or mobile phone that you have previously used to log into your Facebook account.
- Once you get back into your account, learn how to reset your password.
2. Try to recover your email account
- If you signed up for Facebook with your email, contact your email service provider to regain access to the email on your Facebook account. For example, many email service providers have a Trouble signing in? Option on their sign in screen.
- If you regain access to your email, you can finish the steps to reset your password.
3. Try Trusted Contacts
Facebook came up with this smart idea of recovering one's account with the help from the user's selected friends. You can read the detailed steps here: How to Get Back into Your Facebook Account with the Help of Your Friends
Gook luck! Hope this answer helps.