On our project we are allowed to use following licences : MIT, MIT-equivalent, Public Domain and several other concrete licences. I am not able to find out which licences are MIT-equivalent or Public domain lincenses. From the title GNU General Public License, version 2 it is probably a Public domain licence, but I am not sure about this.
The GPL 2.0 license is a copyleft license. This means that it puts major restrictions on anyone who distribute GPL licensed code or who wants to reuse GPL licensed code in another project. The most important rule is that anyone who uses GPL licensed code in their own project must publish their own project under the GPL license itself. So you can't use GPL licensed code in a closed-source program.
You can include MIT licensed code in a GPL project, but you cannot include GPL code in an MIT project. The GPL is definitely not a public domain license. Public domain means that anyone can do anything with it, including using the code in closed-source programs, and without attributing it to the original author. That is absolutely prohibited by the GPL.
Can you use the GPL 2.0 license for your project? Maybe. Best thing to do is ask whoever is setting the project.