Detailed explanations of each panel are presented below.

• There is a line connecting each level of the means for A1, A2, and A3. If we did not consider Gender, then this line would be the main effect of A. In Panel 1, the means differ so there would be a main effect of A. This is not the case in Panel 2.
  
  
• In Panel 3, all the B1s are higher than B2. Thus, there is a main effect of B. Note that A has no effect for B1 or B2. So there is no effect of A or an AB interaction. The latter is because A has no differential effect dependent on B.
  
  
• In Panel 4, A has an effect such that as Year increases drinking increases. Gender (B) has an effect as the B1 line is higher than the B2 line.
  Big Point Alert - The B1 line is parallel to B2 line. Year effects each Gender in the same fashion. There is No Interaction!
  
  
• In Panel 5, A has an effect such that as drinking increases with age for all groups. B has an effect, as the B1 line is higher than the B2 line.
  Big Point Alert - The B1 line is Steeper than the B2 line. Thus, the year can have a different effect dependent on your gender. The lines are not parallel. This is an Interaction.
  
  
• In Panel 6 the slopes are opposite. This is a cute one. If you compute the average for B1 vs. B2, forgetting about Year, then there is no effect of gender. If you average the Years forgetting about Gender, the years don't differ. You would get No main effects. There is only an Interaction. That's why we check it first.