I have REV. G DE1-SoC board. How can I distinguish that which version of Quartus I Should use? I found the information that either I have to download Quartus 13.1 or 16.0. Please find attached file and give me feedback.

I guess you can use any version of Quartus as far as the FPGA device is concerend, but regarding the compatibility with the Terasic provided tools, you will have to contact them and find out if their tools will work with the latest versions of Quartus or if you need to use only that specific version.

Ideally , you can download the latest version of Quartus along with the specific Device files and install them. This would be sufficient to develop for that FPGA on the DE1-SoC board.