Home business........?

With a diploma in apparel and accessory designing and a sew&embroider machine at home, what small business can i do at home (online)? Please suggest some business ideas which require less to moderate investment..

It sounds like you have little to no business experience. However don't let this discourage you. I would suggest taking a business class or seminar specifically pertaining to retail.

The cheapest method of entry into the market would be a website like etsy.com

It is a virtual market place for crafts like you are describing. However, if you want to grow your business to sustain you and your family, then I would strongly suggest learning the marketing and branding dynamics within that industry. It is highly competitive but if you have something unique and popular you could be the next Armani, good luck.