The basin wrench you linked to would be the right tool if the hex nut was 1 or less.
Tool to tighten nut under sink.
How to tighten a nut under a new sink fixture.
Fit the head of the wrench around the faucet mounting nut so the ridged jaws of the claw grip the notches or edges of the nut.
With the flashlight you need to locate the nut that secures the faucet in place.
Operating the basin wrench.
Insert the fixture into the appropriate hole in the sink center it and align it with the back wall.
Clear off the shelves under the sink to give yourself more room to work.
This lightweight tool with durable aluminum inserts handles many aspects of faucet installation including shut off valves supply lines and basket strainers.
Slide the open end of the faucet wrench over the supply tube and push it up to the faucet nuts.
Set your wrench to the correct size.
For a larger nut like this it was designed to be either hand tightened or with a wrench like the channel lock or adjustable wrench you linked to.
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If the sink p trap is in the way remove it by unscrewing the nuts.
Remove faucet nuts with a faucet wrench.
The ez change faucet tool is a multi purpose under sink plumbing tool that works on most faucets.
Abn rigid basin wrench extendable faucet installation tool telescoping plumbers under sink telescopic 3 8 to 1 3 8.
The short reinforced body not only clears spaces but is easy to store.
Slide under the sink on your back next take the flashlight and slide under the sink on your back.
Close up of the faucet wrench.
Then turn the ratchet and it will self center on the nut.
But to use the wrench you would need to first remove the sink from the counter.
In the photo here the head is positioned for loosening the nut use the t bar at the end of the basin wrench to turn the shaft and loosen or tighten the nut.