That will work fine. 16 ft is the limit for a passive extension, or any combo of daisychained passive cables up to 16ft. If you're using a 16 ft active cable with a 6 ft printer cable you'll be fine. Actually the limit for high speed 2.0 with active daisychained cables is 30m (just under 100 ft) That's achieved by connecting 5 x 5m (16 ft) active cables or hubs, with an additional device cable not exceeding 5m - to total 30m. It does depend on the quality of cable though - it needs to conform to the spec of 480Mbps transfer speed and proved a min of 250mA - for high speed 2.0. Not all cables are created equal - generally you get what you pay for.
What you are trying to accomplish is exactly this:
https://youtu.be/RlT2F6DgtjI?t=40s
"The extensions cables built in signal booster ensures reliable data transfer for the combined length of the extension cable, AND your device cable"
In theory, up to a 16 ft device cable after an active extension or hub, but in practice it almost certainly wouldn't work reliably. In your case with only a 6 ft printer cable you'll be fine.
Again though, only if the cable is decent quality.