From track means they can find your source wallet from where you made a transaction. To avoid the tracking of source wallet, you should prefer to use mixers or wallets that have the feature of coinjoin. Even many hardware wallets have coinjoin feature. If you do not know what is coinjoin, then its means that joining/mixing coins so that no one could track the source wallet address.
If you send a transaction from one wallet to another and then from that wallet to the third wallet, everything is being seen transparently on bitcoin blockchain however here we are putting the exchange address in between. This means that the OP will send his bitcoins to the exchange. You can verify from blockchain that he send the bitcoin to an exchange address. However, when he will withdraw bitcoin to another address, the exchange will not use his address as a source, so the connection of his source address will be broken and there is no way to link the source address of the OP to the new address where he send his bitcoin from the exchange.
In the case, which OP mentioned, the reason for this mixing is only personal (and not to hide coins from government / financial sector), the exchange can fulfill his requirements.