My husband had carotid left side operation 4 weeks ago and he still has a very hoarse voice and he find speaking a sentence hard, will this rectify it?

Be seen: At this point i would expect some noticeable improvement so if it is very hoarse, let your surgeon know. But a visit to an ENT to check his vocal chords will be helpful. Sometimes, it does take longer than 6 weeks and even up to 6 months. The nerve that controls the vocal cords sometimes gets stretched and needs some time to recover.

Probably gets better: The nerve to vocal chords is very near the carotid artery. Can be irritated by surgery, result is hoarse voice because vocal chord that side moves poorly. ENT exam will verify this. Most get better-sometimes need months. Speech therapy helps some. If doesn't improve, many benefit from injection by ENT. If aspirating (choking a bit) on food or liquids seek help quick. Hope this helps.