This is not possible. Here's why:
When you install Quickbooks it offers three installation options:
1. company file resides on computer only-- you are installing a quickbooks server
2. company file resides on computer and user runs quickbooks on the computer--installing server and application
3. user runs quickbooks but company file resides on another computer-- installing application only
The quickbooks database manager, as it is called, is a piece of windows software that runs in the background and it is what allows multiple, simultaneous, access to the company file without corruption. It may not be obvious but when you switch from single user to multi-user mode, and the company file has to close and re-open, it is invoking the server software to take control.
Since it is windows software it can't run on a Synology which is Linux. You might think quickbooks database manager can run on windows but the actual company file can be placed on a network share, such as a synology disk station but the database manager won't allow you to run off anything but a local file-- for good and technical reasons.
While it is not possible to use a synology to accomplish what you want, it is an otherwise a very straight forward setup to give a remote user secure access to local resources, be they server, computers, etc. A VPN or virtual private network does exactly this; by the way the disk station has VPN software to act as a VPN server. Unfortunately, there's no simple way to setup a VPN. the best bet is to get someone, your ISP, local tech support etc. to setup your VPN for you.