Yes, it should be more than enough for a web site that is not excessive in size (amount of pages/large downloads) or daily traffic.
For your site to use more than 6000 GB of transfer/bandwidth, it would have to be receiving a large amount of visitors on a daily basis and/or have many pages that are being accessed and/or have large files being downloaded.
Example: Every time one of your web pages is viewed by someone on the Internet, the size of that page goes towards your bandwidth usage. Below is an example of how many times a page would have to be viewed to reach just 40 GB of transfer
page size 30kb = 1,398,101 views
page size 40kb = 1,048,576 views
page size 50kb = 838,861 views
page size 60kb = 699,051 views
All activity on your account counts towards the bandwidth used for your account.
This includes:
It is possible to use much more bandwidth suddenly if your site is featured on a popular review site, you provide large, popular files for download, or other sites hotlink to your files.
You may track your bandwidth usage in Cpanel under General Account Information on the left and in your stats and raw access logs.
You may also stop hotlinking by using Hotlink Protection in Cpanel and you can move, delete, or lower permissions on popular files permanently or temporarily.
Bandwidth does reset automatically some time after 12am on the 1st of every month.