I’ve been slow to understand zero factor sensitivity. I am at a total loss for how to approach such a problem let alone solve it. Help is greatly appreciated!

I don’t want to fully repost the question or violate any agreements, but I would happily take any example of what a zero factor sensitivity is and how to derive such a portfolio from various potential strategies. I understand that one factor varies and the rest are zeroed but am uncertain how to construct such a portfolio given a list of different strategies. Please help!!