The roberts family is shopping for a new vehicle. they are considering a minivan or an suv. each vehicle has three models; standard, sport, or luxury. the family has decided that they want a red vehicle. explain how to make a tree diagram to show their options. how many choices do they have?

So I searched for your question and discovered there where more colors to the car! So for the sake of example, I will give my example, and still answer your question! 

Okay, so at the top of the diagram, you start the basics, 2 cars. 

Next, you want to go into detail, the model, Sports, luxury, or standard! 

Then for each model, you have colors! silver, green, blue, and red.
 

To answer your original question, there would be 6 choices/options to choose from.  
 - Because they specifically wanted a red car, and there are 3 models, and 2 car builds.  Multiply 2 and 3, you have 6, or make a diagram. 

To explain and answer my diagram/example, 
there would be 24 choices/options for the family to choose from. 
-Because there are 4 different colors, 3 different model types, and 2 car builds. Multiply 4,3, and 2, and you get 24!  (You can also just count the colors on the diagram!) 

(To answer the model question I found while searching online, the answer would be 30 choices.) 

The answer to that is 6