[devnull69]

"value" is not an attribute for <img> elements

Try this

$(document).ready(function() {
   $('.not_selected').click(function() {
      // extract the number from the src of the image
      var theNum = this.src.match(/\d/)[1];
      // hide all the divs in white_section first
      $('.white_section div').hide();
      // show only the one with the correct number
      $('#white_content_' + theNum).show();
      // add a new "fixed" class to the current element that cannot be removed on mouseleave
      // remove this class from all other <img> first
      $('.not_selected').removeClass('fixed');
      $(this).addClass('fixed');
   });
   $('.not_selected').hover(function() {
      $(this).addClass('selected');
   }, function() {
      $(this).removeClass('selected');
   });
});

You would need to introduce a new .fixed class that cannot be removed on mouseleave and that should have the same style as .selected (just add another class selector to the same CSS rule)