Firstly, Plants Vs Zombies FREE is one of those games where, if you delete the app and reinstall it, you have to start from scratch. (It happened to me personally). There are also no cloud backup options as far as I know. This means that you'll have to look for a way to transfer the data manually.
There is a guide at https://plantsvszombies.fandom.com/wiki/Backup_guide#Android but you may have to root your tablet, thereby voiding your warranty. If you don't know what rooting is, it's basically modifying your phone/tablet system to gain deeper access to more fundamental things, e.g. if you want to overclock CPU, or edit system files. I recommend researching rooting if you don't know about it already, before moving on - it's quite technical. However, it also says that root "may" be needed, so maybe you won't have to.
If the above doesn't work non-root and you're not keen on rooting your tablet, I found this website: https://www.maketecheasier.com/move-game-progress-between-android-devices/
The second option recommends an app called Helium which could manually transfer your app's data without root. However, there are almost as many 1-star reviews as 5-stars.
I hope that helps. Things might get a bit technical. Make sure you backup anything important before meddling with the tablet's files. Good Luck!