In case you need to do it again in the future, when you look for upgrade path you need to check release notes in the path backward starting from the target version. In your case, you checked 5.4.8's release notes and found you could upgrade to it from 5.4.6, 5.4.7, 5.2.12, or 5.2.13. But it doesn't include your current version 5.2.11. That means you need to get to one of those 4 versions first. Now you need to make up your mind which version you want to get to before getting to 5.4.8. And you decided 5.4.6.
Now, you need to check 5.4.6's release note, which would show you 5.4.4-and above, or 5.2.10-and above. That includes 5.2.11. That's when you can be sure 5.2.11->5.4.6->5.4.8 path would work.
Toshi