What juicy details do you need.
The important bit is front and center: type NM cable, probably without a separate ground wire. This wire has a 60C temperature rating, and is probably just fine for ongoing use except where overheated at terminations.
Ah. Complicated.
The inspector wants me to install a 60A breaker on that, is why.
His argument is that the wire distance is fairly short, and I can use the temperature charts to prove out a 60A breaker.
Exactly why is complicated
Existing condition:
* 50A main fuses upstream, good condition
* 50A subpanel in the closet, in good condition, but FPE Stab-Lok.
* 1960's construction: gas heat, three light fixtures and 7 receptacles per one bedroom apartment.
Insurance company
* FPE is bad: insurance cancelled.
AHJ Field Inspector Says
* Can't have it in the closet any more
* OK to reuse the 3 wire feed.
* But the subpanel has to be 60A per code (because it was replaced)
unless I can prove the feed wire can't support 60A.
================================
The same inspector wants us to change the 12.1 kw electric ranges to 10 kwh ranges, because
he can't imagine why a 50A peak load range is safe on a 50A main, given other loads.
So his view is either we go to 40A ranges with a non-compliant 60A panel. OR go to a 60A panel on the existing cable pictured above.
In the end
we agreed that I'd research the wire type, temperature rating, and "do the calculations" as to the best that can be done with the existing 3 wire feed. Sigh.