‘Work out’ in this context means ‘to figure out’, ‘to try to understand’, ‘to conclude after much thought’. It involves more brain work than just guessing.

In another context it can also mean ‘exercise’ as in ‘I’m going to work out at the gym’.

The Oxford Learner's Dictionaries website is an excellent resource.

to work out - [to exercise]

to work out - [to have a successful result]

to work something out - [to solve something]

to find the answer to something

synonym <a href="https://www.oxfordlearnersdictionaries.com/definition/american_english/solve" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 74, 172);">solve</a>

<em>to work out a problem</em>