I am not sure how tall that is, but it looks like (4) 2" layers to me. What I would do is when stacking the layers, I would stack (2) 2" layers like you would with a regular cake, then your second set of 2" layers would go on a separate cake board then you could stack them all together. This will allow you to separate the layers for easier serving. Make sure to use something to support the layers, like dowel rods and make sure the supports go all the way to the bottom of the base cake.
Looking at the top tier which looks to be 4" tall and the size of the flowers makes me want to guess its six layers.
Thanks guys. I think I will go with four, since she doesn't need a whole lot of cake, and I can use my SPS stuff to stack it. I'll just double the servings for two 6" (2 layers).
The answer will depend on how big the tier is. If it's a 6" round, then 3 layers; if it is a 12" round then probably 4 or even 5 layers.
The bigger around the cake the less tall it will look using the same # of layers.