travelling family of 6. how to get from hong kong airport to mongkok?

Taxi is not suggested. I'd recommend you take Airport Express, then free shuttle bus. I have no idea about your exact destination, but you can get off at Kowloon station by the express train, then change to free shuttle bus K5. The bus will stop in front of Metropark Hotel Mongkok & Dorsett Mongkok Hotel.

The express train has group package tickets with discounts. Since you are in a group, you may choose the most efficient package: 2+4 or 3+3. If you will stay for several days in HK, Octopus Card can be a good choice. To pay with it can enjoy discounts on buses, mtr and ferries.