It all depends on how much light you need and where you need the most. A 4" recessed is usually used for kitchens.

6" recessed is usually used for larger rooms and placed about 6' apart.

IMO a low ceiling in a living space should have 4" recessed lights in order to hide the light source as much as possible.

It will be difficult for us to select the fixtures and locate them without a rough budget and plan.

Light the walls first. The soffit will be a challenge if it's filled with ducts.

Is this a basement?

It's not a basement.  This room has just 2 gimbal lights focused to fireplace  and one in the corner going towards hallway.  To my understanding I know it will need around 8 recessed lights of 75w but I am just wondering if 6 inch will be too big for cieling which is little shy of 8 ft.

We are putting 4" ones in the kitchen that has 8' cieling height. This room doesn't have a whole lot natural light as it's on the north side of the house and with just 2 gimbal lights by the fireplace.  It's in need of recessed light but we are just confused with the size. Can on go with mix of 4" and 6" . Does the cieling height matter with size of light or it's just about wattage

Its generally about the visibility of the light source, lumens and what you are lighting. Smaller fixtures are less visible, more closely spaced and can provide focused lighting. For a low ceiling high lumen 6" fixtures would need to be too far apart and unfocused.

Please show or describe the 4"fixture you will be putting in the kitchen.

This is what will be used in kitchen that has cieling height of 8'

The fixture you posted is not really "recessed" nor is it a "surface mounted" light; it's flush with the ceiling and called a "direct mount" or "wafer" light reminiscent of the early recessed outdoor fixitrues that had a frosted lens flush with the ceiling.

In recent years I have seen these fixtures in developer apartments and condo units and have even allowed them to be used when I was a project manager for a developer but only because that avoided the expense of fire proof fixture enclosures.

If you like the appearance, I would only suggest you ask what the R8 color value is in order to provide realistic skin tones. Many of these things have a negative R8 value. I have often had to call the manufacturer to get that information.

Where can I see the R value. Also if you suggest what kind of lights will be good for this room and kitchen aswell.

When you position your kitchen lights place them 6" inward from the counter edge over work zones for task lighting. Hopefully they're leds with enough power to give you 450+ lumens at the counter.

So for 7 ft 10 inch cieling ( living room) either 6" or 4" should be fine. Also as you can see in the pics , when u stand in the kitchen you can see the cieling of that room as it's 3 steps down from kitchen level. Tia

Thanks .. I think will go with 4 inch ones . It will be challenging because the electrician says can't put lights in the soffit area. Now any advice on  where exactly to place keeping in mind the sectional and tv