This video offers more experience with the use of Karnaugh maps by introducing the concept of a seven-segment display driver and designing them using a four-input map. We also get a chance to use don't cares.
You'll find that a rectangle containing 2 cells will only have one variable drop out. For example, if a rectangle covered only the top left cell and the cell immediately to its right, A, B and C would all stay the same, specifically A=0, B=0, and C=0. D, however, would change from a 0 to a 1. That means D would drop out and you'd be left with a product A-bar anded with B-bar anded with C-bar.
A lot of my students have trouble with this, so you're not alone. Part of the problem is that the hexadecimal digits include A, B, C, D, E, and F, and the segments of the 7-segment display are labeled a, b, c, d, e, f, and g. There's sometimes confusion regarding these labels. The "e" column represents the vertical LED that is in the lower left corner of the 7-segment display. Picture putting tape over all of the other segments on the display so that only the 'e' segment is showing. The 'e' column shows whether the 'e' LED is on or off based on the different patterns of ones and zeros at the inputs. The ones and zeros at the inputs, on the other hand, represent what number (or hexadecimal letter) we're trying to display.