Upper/lower gives every muscle two sessions a week on four days, which is the middle ground between the three-day full-body week and the six-day push, pull, legs week. It suits dumbbells well because each session stays short enough to keep the weights moving.
With dumbbells only, the work has to come from the hands. Presses, rows and curls need no substitute. For legs, the barbell squat and deadlift become goblet squats, split squats and dumbbell Romanian deadlifts, with the single-leg moves doing the heavy lifting once your pair of dumbbells stops being heavy enough for two legs.
There is no pull-up or pulldown here, because neither is possible with dumbbells and a bench. Rows and pullovers train the back from other angles instead.