Instant water heater wiring
You can use that 6/2 WITH Ground wire and run it down through the stud just like 14/2.

I am surprised that it requires 6 gauge wire - What voltage and how many amps ?
I know you mentioned a 60 AMP breaker but that does not tell unit amperage as there are codes and guidelines for proper CB ratings.

That has to be one serious Hot Water Heater - I would have expected #8 or #10.

As for your mention of 14/2 to the boiler unit:


Any chance your old unit was a gas unit ?


That would explain the 14/2 wiring 120VAC for control circuits and gas to do the heavy lifting.
Just an FYI they do make Gas Powered Instant Water Heaters as well.

A 60 AMP breaker might be fine in the same panel as long as your panel will support the additional load. Since you are calling an electrician get quotes an electrician will tell you if your panel will support the added load or if you need a sub panel. This is all dependent on what you already have - a panel model number with pictures of behind the face plate cover would be helpful.

Since your Instant Water Heater is 220V you will not need an AFCI breaker, I would recommend a GFCI breaker.