I purchased this plant from Market there was no mention of it's name but i liked it very much. Any one know whats the name of it and whats the best way to propagate it.
These look like what are commonly known as 'pot mums', the type often sold by florists, market stalls and garden centres; in the UK, these are sold only in autumn and are intended as temporary autumn bedding up to winter. They're intended for instant colour, either indoors for a short period, or outdoors; they are treated with hormones to keep them short and bushy, which means if they survive and grow next year, they will revert to the usual growth habit, which will be much taller and generally bigger plants, sometimes with the same type of flowers, but often with larger and possibly differently shaped flowers. Depending where you live and your winter temperatures, and the type of Chrysanthemum they actually are, they may not survive harsh winter temperatures outdoors, but will flower on until it gets really cold. Unfortunately, taking cuttings still means you'll get the taller, larger version of these plants, so if its the small, dense flowerheads and lower height you want in your cuttings, that's not what you'll get. More information on pot mums here https://homeguides.sfgate.com/can-plant-potted-mums-outside-90378.html
If you do want to try cuttings anyway, there's a guide here but you need to wait until blooming is finished https://homeguides.sfgate.com/grow-chrysanthemums-cuttings-46518.html