Read the reference cell
A two-factor model is fitted with contrast constraints. Level 1 of each factor is the reference. The estimates are \widehat\mu=10, \widehat\alpha_2=4, \widehat\beta_2=-2 and \widehat\gamma_{22}=3. There are no other levels.
Write the four estimated cell means. What is the effect of moving factor A from level 1 to level 2 when factor B is at level 2?
The four estimated means are \widehat\mu=10 at (1,1), \widehat\mu+\widehat\beta_2=8 at (1,2), \widehat\mu+\widehat\alpha_2=14 at (2,1), and \widehat\mu+\widehat\alpha_2+\widehat\beta_2+\widehat\gamma_{22}=15 at (2,2). Moving factor A from level 1 to level 2 while factor B stays at level 2 changes the mean by \widehat\alpha_2+\widehat\gamma_{22}=7, from 8 to 15. The main-effect estimate \widehat\alpha_2=4 is that change only at the reference level of B.