How can i list my vocabularies and their terms in this way . Is there a module that can help me to do this . or i should go with custom VIEW and jQuery.
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You can do with Taxonomy Term Reference Tree Widget module.
This module provides an expandable tree widget for the Taxonomy Term Reference field in Drupal 7. This widget is intended to serve as a replacement for Drupal's core Taxonomy Term Reference widget, which is a flat list of radio buttons or checkboxes and not necessarily fit for medium to large taxonomy trees.