In order to provide the correct solution for a problem, the problem must be articulated precisely. Kidlin's law reminds us why this is important:
"If you write the problem down clearly, then the matter is half solved."
To do so, be relentless on the details and the use of words. Words make up our perception of reality therefore it is important to be precise. Repeat your understanding of the problem back to the briefing party as a recap in order for both parties to agree upon the exact and precise description of the problem at hand. Use visual aids such as (digital) whiteboards if needed to support your interpretation.
Another way of thinking about this phase of articulating the problem can be found in Ben Horowitz' book "the hard thing about hard things" on page 124 even though he attributes the quote to Tony Robbins.
"If you don't know what you want, the chances that you'll get it are extremely low."
In other words — confirm with the client they have a crystal clear idea about what they want. This can be the problem to be solved or the desired outcome a solution should generate. If this is not clear your first task is to help them articulate this. Otherwise it will be nearly impossible for you to create a satisfactory outcome.
Once the problem has been articulated clearly and precisely you can start to "work the problem". Working the problem is a concept brought to my attention by Chris Hadfield in his book "An astronaut's guide to life on earth."
"Working the problem" is NASA-speak for descending one decision tree after another, methodically looking for a solution until you run out of oxygen.
Apply this by deconstructing the problem into smaller pieces and solving them individually. There is no such thing as a single problem. Every problem is a composition of smaller problems. Once the problem has been scoped clearly, you can work the problem by solving each of the sub-problems.