How to make a Karnaugh Map with "don't care" inputs?
Here's how to create the K-Map for the Q output.  Remember that you need to do a separate Karnaugh Map for each of the three outputs.

inputs    output 
A B C D | Q
0 0 0 0 | x
0 0 0 1 | 0
0 0 1 x | 0
0 1 x x | 1
1 x x x | 1



0000 = x. This first line is standard. The "don't care" is an output. Simply put the "x" in the appropriate place.





0001 = 0. This next line is also standard. Put the "0" where it belongs.





001x = 0. The third line contains a "don't care" input. In this case, there should be an output of "0" for both 0010 and 0011. Insert these into the map:





01xx = 1. Similarly, the fourth line states that there should be a "1" in all of the following cases: 0100, 0101, 0110, and 0111. Put these in the map:





1xxx = 1. Following the same reasoning, the last line does the following:




Now, do the same for your R and S outputs!