Can anyone help me understand how to implement a karnaugh map using multiplexers in logism?
You can use a 16:1 multiplexer where A,B,C and D are the address lines and you set the appropriate (1 to 16) input lines to either 1 or 0 to get your required output. The minimal result from the karnaugh map doesn’t really help if you are going to use a multiplexer. This is the most useful formula in your question to aid you: -


  f = Σ(6,8,9,10,11,12,13,14)