Misconstrue

Misconstrue means to arrive at an incorrect understanding of something said or done.

I wonder if misconstruing the was to a problem's solution means to make it impossible to arrive at the solution

It is sometimes said that the first step to finding a solution is to understand the problem, so if the problem were misconstrued it might indeed hinder the search for a solution.

might?!
I asked if it does make the arrival at a solution impossible.

If you misunderstand a problem to start with, does that mean you can never find a solution?

Doesn't it?

You might continue to look in the wrong place and never find the solution. On the other hand, you might stumble on the solution by accident, or you might realize you were getting nowhere and go back and re-examine the problem and spot your mistake.

So does it mean it complicates the arrival at the solution to the problem?

In your original sentence you could replace misconstrues with confuses the nature of
a characterization "confuses the nature of a problem and the way to its solution"
It's very likely that it would complicate solving it.

So, it confuses two things:
1the nature of a problem
2.the way to it's solution

right?

Why did you choose the verb 'confuse' over 'complicate' in number 2?