User side

In My Account page, users can track all the requests sent to the administrator.

My account page

 

If the administrator has replied to user’s request with a quote proposal, the Accept and Reject buttons will be available, like in quote #367 in the above image.
If the quote is accepted, the user is redirected to Checkout page to complete the order. It will then appear with the accepted status in the list (quote #365).
The user might not complete the payment immediately after accepting the quote, then a Checkout button will appear like for quote #363 in the above image.
If the quote is rejected, it goes to rejected status and cannot be resumed.

Users can have access to the quote detail by clicking on the quote number in My Account page.

Quote details

If you want to remove the Totals column, enable Hide column total option in YITH Plugins > Request a Quote > Request List.