First check you local code. In my area, a fence can only be 8 foot tall and no more.
Secondly, this project is easy IF you have wooden posts, and more of a challenge if you have metal posts. the sistering or tying on is easier with the wood.
Thirdly, if you are in an area with heavy wind, then this might be more complicated.
I am in an area with very strong Spring winds. When I tackle a fence extension job like this, I usually do only lattice. I sister pressure treated 2x4's on either side of the wood post up about 2 feet to the 8 foot marker, then create a long 8 foot post to post frame. Then I cut or rip heavy lattice in PT wood and slide it into this frame. then attach the top 2x4 cap. Then get some PT quarter round and frame out the lattice on both sides. This concept allows the wind to go through and give some privacy. Then I instruct the homeowners to begin a vine planting campaign like trumpet vines or such and begin a natural toper.
In conclusion, Mike if you want to do this job right, you should take up that section of fence and just build it to 8 feet tall to hide that window view.