Pull only specific rows and columns from a table

I want to copy certain columns from a table, but only the cells where they cross specific rows. For example, I want to pull columns A,C,F but only where they intersect with rows 2,6,7,and 10. So the new table would have A2,A6,A7,A10,C2,C6, ect. Is there a way to do this without hand-copying or re-typing? I haven't worked much with tables before.

This is for a reference chart I made myself for a game where you place buildings and get (or lose) points based on which buildings are nearby. The rows and columns have the same list of headers: columns are what I want to place, and each row shows how many points each existing building would give. I want to make smaller tables with a few buildings and how they affect each other, such as Harbor, Dock, Lighthouse, and Fisher which all go in the same areas. So I would want to pull just the spots where the columns and rows for those 4 intersect.