Will this chain work on my bike?
It will work adequately on your 6 speed rear cluster.  Its basically 8 speed chain which is identical width to 7 speed chain, and its "good enough" for 6 speed.

Curiously, on a supplier's website for HG40  I notice this line:


  Shimano Altus HG40 6-7-8 Speed Chain
  7.3mm chain width, optimised for 7- and 8-speed HG drivetrains


6 speed is 0.5mm wider but given the tolerances of the day, that should work adequately.  You have to move the derailleurs a tiny bit further to make a shift if its friction shifting.  The FD cage may need to be closed up slightly.

Finding 5/6 speed chain will be interesting - even KMC's own chain checker only lists 8 speed chain as the best option.  http://www.kmcchain.eu/chain-road_cross-multispeed-5_speed

Apparently "clarks CL20" is 5/6 speed chain and may be found at various on-line suppliers.

6 speed is a comparatively old standard and is way less common now, so not worth printing on the packaging?

As per https://en.wikipedia.org/wiki/Bicycle_chain#Width


  6 speed – 7.8 mm (5⁄16 in) (all brands)
  7 speed – 7.3 mm (9⁄32 in) (Shimano HG), 7.1 mm (9⁄32 in) (SRAM, Shimano IG)
  8 speed – 7.3 mm (9⁄32 in) (Shimano HG), 7.1 mm (9⁄32 in) (SRAM, Shimano IG)