What is the maximum number of workstations the subnet mask 255.255.240.0 can support on the local subnet?

By using 255.255.240.0 as a subnet mask you have 4+8 bits remaining, that can be used for host IP addresses. So you have 2^12 IPs - 2 IPs = 4094.

This "minus 2" IPs are because first IP is always the IP of entire network and last one is a brodcast address. None of them can be assigned to a particular host.