Transforming a private key to a public key does not require the network. It's only cryptography. The network does not do any computation for you to give you the answer.
An easier solution using Node.js:
> const Wallet = require('ethereumjs-wallet');
undefined
> Wallet.fromPrivateKey(Buffer.from('208065a247edbe5df4d86fbdc0171303f23a76961be9f6013850dd2bdc759bbb', 'hex')).getAddress().toString('hex');
'0bed7abd61247635c1973eb38474a2516ed1d884'