The quick answer is you've nothing to worry about. BUT there is a "process" (pun partially intended).
I'm going to assume that you are going to (or already have) download the latest Lightroom Classic application (not Lightroom Desktop which is a different application). When you go to open your current catalog, you will be notified that your catalog needs to be updated, click "Yes."
Notice though that when you start looking at your photos, you will be seeing an exclimation point ("!") on the bottom right of the image in Loupe view. This is letting you know that the Process Version for your image is not current. Let me explain what's taking place here. As Adobe has worked on and improved their ability to interpret the data in an image, it uses several rules (officially called a Process). Over the years these rules have changed, they are now on Process Version 5. Any work you've done will be saved with the version that was used on THAT image. Ergo, the exclamation point is letting you know that there are new rules that you can use that might make the image look better. However, if you switch to the new rules, your image will look worse because Lightroom is looking at the corrections made with different rules and those will look "wrong" with the new rules. At that point you can play with the updated Basic sliders to get your image looking the same or probably better because of the new Process Version. (Note: As a side point, Language is filled with examples on how words are used and interpreted like this all the time).
Anyhow, if you wish to experiment, go to the Develop Module and select the bottom one (Calibration) and you will find the various Rules (officially called "Process") there as shown below.
If you want to import all the photos in the LR6 catalog to Lightroom 3.2.1, you can use the File>Migrate Catalog feature, which will "import" all the images including edits and other metadata.
If you only want to import some of the images from the LR6 catalog, you could open LR6 then select all the images you want to import to LR 3.2.1, then do Cmd/Ctrl+S to write existing metadata to XMP. Once that's done, close LR6 and then you can import those images into LR 3.2.1 and the associated XMP data (which includes the edit data) will be read and imported also.