A few strategically placed taller bushes.

A tree. Site it so that it hides the view you want to hide.

Are you prohibited from installing a second 6’ fence about a foot in on your property?

A couple trees or columnar evergreens strategically placed will give privacy.

Those screens look great! I don’t know why you seem fixated on changing the existing fence to solve your problem - those screens can be placed anywhere on your property. Even right next to your deck or where you want to put a bbq pit.

Is there a concern about the gutter directing water right to your proposed spot?

Jilly, I am gonna steal your screens ideas! I need something to fill a bland area and distract from my neighbor’s garage. Thank you 😊

A tree. You want a tree. Plant it directly in the site line between you and them. Even “slow growing” hardwood grow rapidly when they are young. I have oak trees planted four years ago that are now serious trees. Well teenagers at least.

Love the screen idea from Jilly.

A second fence inside your property line will be a nightmare. There is a reason they are called spite fences. There is no way to weed in that area between the two fences and you and your neighbor will have weeds there.

I personally dislike looking at wood fences. I’d plant along the entire span of fencing and then create a curved garden bed with different height flowering shrubs in front of the hedge. You could even intersperse some interesting trees such as Japanese maple. Yes I realize that they are deciduous but you and your neighbor are probably less like

Ooops! Less likely to be outside in the winter. Think of this as an opportunity not only to obscure the view of his house but also to obscure the view of your fence as well.

Cameron O'Neill - Arborvatae is your answer. We have them to shield a neighbors house form our view. They were planted at 6" and 2 years later they are growing taller. This next year will be the year that they really take off. Take a look at THIS Video.