I have a really old desktop with an intel pentium e2160 and 2 gb ram. Can I run elementary os on it?

To tell you the truth, your CPU and RAM are not enough. I also have a computer like you. The CPU performance of this model is so weak that it will run full load for a long time when decompressing a slightly larger compressed file; however, your RAM can only barely run lubuntu. It is inevitable that computers with this configuration will get stuck when running. Therefore, it is recommended that you upgrade the ram to at least 4GB and upgrade the CPU, so that you can run lubuntu, xubuntu and windows 10 x86 more smoothly. You can also choose Windows 8 / 8.1 or LTSC, which is smoother than windows 10. Of course, you can run these systems without upgrading the hardware, but it will be very slow.

You should be able to run elementary os on 2gb ram and 1.8ghz cpu. But in you might face lag when you open a lot of tabs in browser or trying to multitask in 3 or 4 apps. In any case, if it doesn't work out the way you want the. You can try other lightweight os like: lubuntu, unbuntu mate etc like those or if you want arch-linux then manjaro xfce.