Both of them are correct.
But "give a description" is a collocation in English. It means you describe sth you may know it by oral or writing
"make a description" is not a collocation, it may be from the structure "make +O+ V_bare" or sometimes it also means you have to write a description of sth, for instance an essay (something like this :D).
Generally, to make a description you should have ideas, but to give a description you just describe sth you may know :D
EX: How to make a good video description? or Make a description of an ideal friend--> your ideas
Give a description of your job --> you know your job and you describe it :D :D
it's just from my experiences I summarized in the learning process :D :D