The "solution" depends on what's causing the behaviour - there can be so many different reasons for destructive behaviour, from separation anxiety, to over (or under) stimulation, to poor environmental management.
It's pretty much impossible to "puppy proof" an entire house, so you maybe need to look into crate training, or leaving him in a "safe space" like a hallway or utility area where he can't destroy anything or potentially hurt himself. Many dogs get anxious if they have too much "space" as well, so even something like a cosy bed or den area could help, with a baby gate blocking his access to the rest of the house. If other people are home, he needs to be supervised or left in his "safe space".
I'd also look at what happens before you leave him - has he had a good quality walk, been to the toilet and eaten, for example? Is he "tired" enough to settle on his own or is he still a bundle of energy? Does he settle when you're at home with him or does he still need to be managed a lot?
There can also be a fine line between over and under-stimulating some dogs - mine can struggle if he's had a walk with lots of ball throwing or playing with his friends, for example, as his adrenaline is way up and he just can't relax. I find a calm, sniffy walk works much better to calm him down if he needs to be left alone as he struggles a bit with separation anxiety.
It may be worth getting a camera to see what's happening when you go out - is he restless? Anxious? Barking or whining? How long does it take between you leaving and him becoming destructive, for example? It could be that he's not happy being left on his own, in which case that needs to be worked on, or it could just be that there's too much "temptation" for a young dog to resist 
Sorry, didn't realise how long that was when I typed it!