The 0 makes a 6-cell region by itself. This creates a wall by the nearby 1.
Then, make sure not to block off any cells where they can't be part of 6-cell regions:
the 4 clue does some work - if it went up to join the 2, it would stop the 2 from making a region.
And we can do something similar with the 4 clue down below. (I also notice that the 2 in the bottom left is already satisfied.)
We can complete the bottom-right corner:
The 4 clue going up and right would block off the region under it. And if that region doesn't take both cells next to it, it blocks off the one it doesn't take.
The 2 near the bottom middle cannot join with the other 2, because the region would be too large.
Now we've finished off a clue:
We've both of that 2's walls, so it claims the other three cells next to it; this makes the bottom-left region complete.
The chokepoint on the left blocks off six cells.
Putting a border on the left side of the 3 would cause it to gain a fourth wall. Putting a border on the right side of the 3 would either block the 2 region or cause it to merge with the 3 and be too big. So the 3's remaining border must be on the bottom.
This completes the 1 region, and the rest of the puzzle falls into place. The solved puzzle: