using System; is useless here.

so simple and easy understand

why double?! too much memory

I have adjusted the description. Thanks!

Unless you want to teach users about building strings, there is no reason why the output needs to be a string. If this kata is supposed to be beyond 7kyu, then the target audience already knows how to do that. There are perfectly good datastructures to represent grids/matrices; strings aren't one of them.

I suspect English may not be your first language (no worries), but this sentence is awkward to parse: The first four values in the array are to the right of Grid (from top to bottom). The remaining four values are below Grid (from right to left).
A better phrasing might be "The first four values of the input array will be the target sums for each row, from top to bottom; the last four values will be the target sums for each column, from left to right."
I'd also recommed specifying that the input will always consist of 8 values and the game will be played on an 4x4 grid (i.e., no need to write a solution for an arbitrarily sized board)

I'm afraid to sound stupid, but is this best practice?

there are others

https://www.codewars.com/kata/59cc4c5aaeb284b9a1000089 ?

I'm 100% I've solved an exact same task in the past.

Ruby 3.0 should be enabled (Refer this for more detail)

I think they're sufficiently different as there is no information of chunk distribution, only the total length of things in the particular row or column is given.

nice

Also similar with '6x6 or 7x7 skyscraper'. IMHO very nice type of puzzle actually.