며칠 어떤 사람인지 파악하고 자신이랑 성향이 안맞는다 싶으면 선을 긋기도 해요.
파악하다: grasp, understand, assess, figure out
성향: inclination, disposition, tendency
성향이 안 맞는다: not compatible in disposition
며칠: abbreviation 며칠 동안 or 며칠간. For a few days
어떤 사람인지 파악하고: figure out what kind of person (he/she) is
자신이랑 성향이 안 맞는다: not compatible in disposition with himself
싶으면: if it turns out that ...
선을 긋다: "draw a line"; reject and stay aloof; keep someone out
-도 하다: does (something) sometimes
So, if we assume "he" is the subject (it could be "I" also),
(He) figures out what kind of person the other is for a few days and sometimes keeps (him/her) out if (he/she) turns out to be incompatible with himself.
Simplifying a bit,
(He) assesses the other's personality for a few days and (sometimes) keeps him out if deemed incompatible with himself.