How to get the Date, when particular field of a node is equal to some value? I have Content type called "Items", in that i have select list field for status referencing to Taxonomy terms(delivered,hold,dispatched etc.) .
 I want to store the date in some custom table when the item is "dispatched" and use that date in some other code.
 Which is function in which i can write logic to store date in table?  or any other way i can get dispatched date of the item?
You have to use one of the events described in Entity CRUD, editing, and view hooks.

One example from the documentation:

function hook_ENTITY_TYPE_update(Drupal\Core\Entity\EntityInterface $entity) {
  // Update the entity's entry in a fictional table of this type of entity.
  db_update('example_entity')
    -&gt;fields([
      'updated' =&gt; REQUEST_TIME,
    ])
    -&gt;condition('id', $entity-&gt;id())
    -&gt;execute();
}


You can get the original field values from $entity-&gt;original-&gt;status and check if the status has changed.