On the day of Arbaeen can we attend to our wordly affairs like going to office or working from home? Or like the day of Ashura we should avoid it.

Definitely Ashura has a greater sanctity, so one can go to work on Arba’een day. But it’s recommended not to go to show out love and grief for the family of Imam Hussain (a). I have not seen a hadith that specifically says not to work on Arbaeen, but we have hadiths that tell us not to work on Ashura day.