Mint should already have either evince or xreader pre-installed for reading pdf files.
But if you MUST have the "Adobe" reader, hit
Ctrl+Alt+T to open a terminal, then run the following commands in sequence:
sudo apt-get install libxml2:i386 gdebi-core
(enter your password when prompted, then hit enter)
then:
wget ftp://ftp.adobe.com/pub/adobe/reader/unix/9.x/9.5.5/enu/AdbeRdr9.5.5-1_i386linux_enu.deb
then:
sudo apt-get install ./AdbeRdr9.5.5-1_i386linux_enu.deb
you should now find it in the main menu at:-
Menu > Office > Adobe Reader 9Note:- Please remember Linux commands ARE case sensitive, so be sure to enter the commands EXACTLY as above

If for some reason it doesn't start from the menu the first time, open a terminal and run
when it starts, close it and try from the menu again.