Can I edit two files then make one commit using GitHub Web-based editor?

There is a web-based workaround:

1. Create a temporary branch, switch to it;
2. Edit multiple files, commit each file separately;
3. Make pull request;
4. Under Merge pull request button, choose Squash and merge (if the repo allows it), then confirm merge;
5. Delete temporary branch.

I use this method on a PC which I don't want to install git on.

The new and better approach is to use the GitHub integrated online VSCode editor.

1. Press　. (period) on your keyboard when viewing your repository. This launches an in-browser VSCode instance (on github.dev).
2. Make your changes across multiple files, just as you would do locally.
3. Use the sidebar on the left to select the Git menu, and commit/push through the GUI as normal. You can also create a Pull Request there if you don't have write permissions.

Yes there is a way to edit 2 files, when you've already edited your first file in the web browser view of GitHub. It's based on the instructions here:

https://webapps.stackexchange.com/questions/95940/how-can-i-change-multiple-files-and-submit-them-in-one-pull-request-on-github

The summary and clarified steps are:

1. Edit your first file, by clicking the Edit icon in another user's repository. Save this edit in your first commit. GitHub will automatically create a new branch/fork for you, like "patch-1".
2. Do not create a Pull Request yet.
3. [This part is the most difficult, because it's not obvious] Go to the list of repositories in your profile, at github.com ➔ click icon at top-right ➔ Your Repositories. Then go to the forked repository that you've just made, and switch to the "patch-1" branch.
4. Continue making changes to another file, and commit it to your "patch-1" branch. When you are done, click the "Pull Requests" tab near the top, then click Compare & Pull Request or Create Pull Request. You should see your 2 commits in this Pull Request.
5. If you don't see a "Create Pull Request" button, open a URL like this in your web browser: https://github.com/TargetPerson/TargetGitRepo/compare/master...MyGithubUsername:patch-1
6. This will show a view to compare your changes to the original target branch in the other user's repository. Then press the Create Pull Request button.