Let's say that I have a website at http://example.com (hosted and name registered at HostMonster).

Then I buy a domain name called "example.net" from GoDaddy. Can I set up in Godaddy to forward this domain name to a subdirectory of example.com.

So I want whenever someone visits example.net to be redirected to web pages on http://example.net/newsite But on the browser address bar show always "example.net".

To the user, it should look like example.com and example.net as two different sites.

Hostmonster should have an "addon domains" feature in the control panel. Use that to have example.net hosted on your shared hosting account. Then change the domain's nameservers at Godaddy, as instructed by Hostmonster when you bought the hosting account.

Hello. I Think that first of all your new domain name need to be hosted and 301 must be used to forward the users fronm new domain to subcategory on the old one.

With correct .htaccess configuration and mod-rewrite you could achieve this, but why would you? This is actually considered cloaking (and thats what it is) to most search engines.