Quick legal check:
Do you own the computer?
How old is you stepson?
Quick answer:
If he only deletes the browser history, the recent sites will be in the browser cache (if he doesn't delete that too). It is quite easy to misinterpret the sites in the browser cache because of links to advertisers, so be careful. There are also umpteen sites where the URL name does not reflect the actual content, and are actually harmless.
Context: When posting a Personal Computer question, it always helps to post some detail about the computer and its software - especially the Operating System and version, how it is connected to the Internet, and what Anti-Virus and Internet Security programs you have installed already.
Is this a PC shared by the family? Do you have his password? Do you have the Administrator account password (unless your stepson's account is already the Administrator)?
Monitor?: In this case it would also help to know if you have a second computer which is on the same home network and which could be used to "monitor" the other PC. ... Or perhaps do you mean "analyse" or "record" rather than "monitor"?



