Update the last modified date when there is a new case comment

To update the last modified date on the Case from new Case Comments, follow the below steps:

1. Create a Date/Time field on your case. This field does not need to be on the page layout.
2. Create a Workflow Rule on the Case Comment that triggers every time a record is created or edited. 
3. As Workflow Criteria, use a formula that will always be true. You can simply type "True".
4. Add a field update that will assign a value to the field you created earlier on the Case. The value will need to be assigned through the formula NOW()
5. Save.

This will ensure that, each time a comment is added or modified, the field you created will be updated and will contain the date/time of the last comment. This will in turn update the Last Modified Date field on the Case.

This can also be accomplished with the process builder: 

1. Create a Date/Time field on your case object. This field does not need to be on the page layout.
Create a process builder on the Case Comment object that triggers every time a record is created or edited 

2. Set Define Criteria for this Action Group to "No criteria—just execute the actions!" Immediate actions choose "Select a record related to the CaseComment" 

3. Select Parent ID, then choose the field you created earlier. The formula will be NOW() <state exactly where in the article to add the text> Can be added at the end of the article

Related Information
Create a Workflow Rule
Create a Process