How long does l-thyroxin (one 0.75 microgram pill per day) need to lower tsh level? my cd3 bloodwork result for tsh is 6.17 (norm: 0.3-3.5)

Mildly low: Your TSH is only mildly elevated. Your thyroid level (free t4) is likely to still be in the normal range. If you recently gave birth, this could be a temporary problem (post partum thyroiditis), and may not require treatment. Taking 0.75 mg of thyroxine should correct the level within a few weeks (though you may not feel any different).