actually broken links can not be solved by webmaster tool. you can only check over there that your links that its broken or not, its the server problem and a admin of site can solve it. when search engine does not found a file for the site's page then it shows page not found. and it can be solve the web master only.
A broken link is a link that doesn't work, often resulting in an error page. A broken link happens when the link points to a web page that has been deleted or moved. Fixing or removing broken links from your website allows search engines to completely index and tells search engines that your website is not being neglected. As part of the optimization process we will test your Website's links and repair or remove any broken ones. Make use of "Disbow" tool to remove broken links