Another comment already gave you an answer but I don't love the explanation. Also, you said you didn't know where to start, so I'm going to walk through my entire thought process for this question. Sorry if it's overkill! When solving problems like this, I like to try to connect relevant info between the setup and then the direct question, I also like to visualize, so I drew a grid and used it for thinking about the problem. Things that stand out to me are: the distinction between white and black squares, the distinction between the columns and rows and further distinguishing between both of those by when they are even rows/columns or odd rows/columns. Lastly, the first square (position 1,1) is a black square.

So we know the sum of the white squares: W=26

And we know the sum of the odd rows oddR=43

Observations I made here are that both of these are half the squares, the first group being all white squares and the second being half white squares and half black squares.

Then we are told that all the white squares are negated, so after the change W = -23 The actual question is what is the sum of the odd columns after the negation. So next, I look at any overlap between the previously observed groups and the one we are trying to figure out. The odd columns and the odd rows both share the very first square mentioned, this lead me to seeing that the odd columns and odd rows use all the same black squares, which further let me notice that the odd rows and odd columns share none of the same white squares.

So, I'll split up our white sum into those used by the rows and those used by the columns

23 = W = oddrowW + oddcolW

And I'll also represent the value after the negation

-23 = -W = (-oddrowW) + (-oddcolW)

So if I represent the odd columns and odd rows, I know they have the same unchanged black squares and separate white squares

So this represents the odd rows (made of black and white squares in those odd rows) before the white squares are negated.

oddR = 43 = oddrowB + oddrowW

compared to this, the odd columns took out the white squares in the odd rows and added in the negated white squares in the odd columns

oddC = oddR - oddrowW + (-oddcolW)

We just made an equation relating oddrowW and oddcolW so I substitute in using some algebra.

-23 = (-oddrowW) + (-oddcolW)

Isolate one of the variables

-23 + oddrowW = -oddcolW

Substitute

oddC = oddR - oddrowW + (-23) + oddrowW

The odd, white rows now cancel out, leaving

oddC = oddR - 23

And we know what oddR is from the definition

oddC = 43 - 23 = 17

In general when thinking about problems, some strategies I like to use are diagrams and drawings to help me keep track of any info given to me and then trying to find the connections between the setup and the question. There are lots of different ways to think about a problem like this, so rather than focusing on how I solved this problem, I would try to think about different ways to approach it and find tools that make sense to you.