How I can pass more than one attribute values at a time to filter products like attached image instead of filtering products using default functionality of selecting one attribute at a time?
This is a brad subject. I doubt you will get a fully working solution as an answer.
I can recommend you 2 extensions that I've used before. Both of them work nicely. They are not free but I think they are worth the money.
Both of them do what you need and much more.