The corners have to be cut at 45 degree angles to fit together with a miter saw. Then if the wood floor is lower, you will have to cut down the baseboards height by ripping some off the bottom of the baseboard with a table saw.

x2 what Chromatic said and use the shoe molding on the vinyl floor. What is the difference in height between the 2 floors?
It looks like vinyl floor is much lower and you will need a reducer there. If there is a big height difference, they should have used next size underpayment to match adjoining floor.

Wow, I think you're right GN, now that I look again, it's the vinyl that is lower....optical illusion. In that case, now that the vinyl is already down, you don't have the opportunity to make the underlayment thicker, right? I would look into what GN said. Put a piece of square wood that is close to the same thickness as your baseboard and the same height of the shoe moulding (or quarter round) under the baseboard along the wall. Then hide the fact it's there by putting the shoe moulding or quarter round in front of it. Not the best solution, but a solution.

Instead of square wood, get next size base of the same profile (so if you got 3" base on top of the hardwood, get 3 1/2 or 4" base) tall enough to reach the top and when you get to the transition point, miter only to the hardwood floor, the rest will go straight down and use a step down floor reducer for the transition.

Good luck