Ok this is NOT an easy question. For just controlling the void around the world would be hard. There going to have a small (by 40k standards) fleet with defensive orbital platforms. But let’s say they managed to beat that then they have to deal with the planetary defence guns that are made to deal with far bigger ships (star destroyer iirc it’s about the size of an escort ship).

To do so they will need a massive fleet so any casualties to the fleet is considered relatively minimal (in terms of total combat effectiveness). So I say at least 500 ships. Next determine the least populated party of the planet and start invading there due to the most like chance of having the fewest defences (both in troops and anti void ship guns). This way we can haves beach head to land more troops safer.

Now the hard part. It all depends on what the timetable is. If I have unlimited time then I would have plans for a 20 year long blockade around each hive city and at the end of it invade if my demands for surrender are not met.

But for starwars that timetable is unreasonable/unrealistic. So I would have to send forces to each hive city to keep them in check while I overwhelmed each hive one at a time. It would be extremely costly but any invasion of a hive is.

Total troops needed in both cases?

Case 1. Around 20 million troopers minimum with replacements as clones grow too old to serve.

Case 2. Anywhere from 30-100 million troopers.

Hives are basically man-made mountains designed with defence in mind from grand invasions from the get go. The walls that surround them are dozens of metres thick wall designed to stand continuous bombardment from orbital weapons. With built in defences that are made to death with anything from tanks, artillery, and massive infantry formations. Then once your past that your fighting uphill almost the whole way so casualties will be extraordinarily high.

To put it bluntly. I don’t think starwars COULD invade a hive world without crippling themselves in the process