Will this memory card be compatible for my Nikon D3200?

16gb SD Extreme SanDisk SDHC Memory Card 45MB/sec (Class 10) - 16GB

My previous memory card is faulty and I don't want to waste money and make the same mistake again, so will it be compatible?

It should do. I wouldn't see why not if it fits then its the right type of memory. Though i have no personal knowledge with the sd car nor camera.

Any and any SD / SDHC / SDXC card should be fine for still images
As for videos you will need a Class 10
So yes, your selection is perfect

Only that I would hate to lose 16 GB worth of takes in one go
I would get 2 cards of 8 GB instead

Don't know what you mean by "same mistake again"
But make it a habit to routinely upload your card's contents to your computer
Then format the card 'in-camera'
Keeps your card healthy

You can check your owner's manual for details but yes, it should work just fine.

However 32gb is overkill if you're following proper procedure which is: upload after every shooting day. Once you know your files are safe, format the card in the computer. If you do it properly you shouldn't need anything over 8gb. If you're doing lots of video on a particular day a 16gb but that's it.

On page 177 of your user manual and you will see that your camer uses SD, SDHC and SDXC cards. Class 10 would be the best to buy if you intend to shoot video or in the continuous shooting mode