I want to make the application like below.
First there is a page with four radio buttons. The user clicks on any of the radio buttons but doesn’t save and he goes to another page. Then if he comes back to same page with the radio buttons it shows the selected radio button before he goes to another page.
How can I do it by using jQuery and PHP?
You can either save the value in a database, or in a cookie (with javascript, jquery: settings cookie with jquery
EDIT: As palasso said, you can also use php sessions instead of the cookie, all depends on your need.
For example, the user can change the cookies you created (they are just .txt files) and alter the information within.
In your situation, this dont seem to be a problem (becose the cookie depends on the checkboxes the user clicked).
So, you should go with database storage if:
Else, go with cookies/session.