Reduce the model sequentially

I was given an ANOVA table and asked to reduce the model sequentially.

Here, Mix and Plasticizer are two main effects, Run is a block factor so is a random effect.

I searched the online resources say: When reducing the model sequentially, you typically start by assessing the significance of high-order terms and then proceed to lower-order terms if necessary.

The solution for this homework is the model is reduced in the order: Plasticizer* Mix, Plasticizer, Run*Mix

Any ideas about why in this order? If we start from the largest p-value interaction, that would be Run*Mix first?

Thanks!