Hi everyone,
I have looked up in a wide variety of dictionaries for this phrasal verb[work out for yourself]. However, I have checked out many senses which one is more suitable for this sentence.

"If you try to work out for yourself the subject, verb and object - then ask someone if you are right - you will understand a lot more than by just asking for the answer."

Here: to work sth out - (esp BrE) to think about something and manage to understand it.

Examples:
The plot is very complicated - it'll take you a while to work it out.
I'm sure you can work it out for yourself.

[taken from Longman Dictionary of Contemporary English]

Yes, the normal use is the one you (@Acooperator) have in your quote. Also the one customic presents.

I've just thought of a couple of slightly different uses, not strictly as phrasel verbs.

He works out at the gym twice a week. / To work out physically/ training.

Things will work out okay in the end/ Things worked themselves out in the end (everything will be fine eventually)

Just put a plaster over that splinter - it'll work itself out [it'll come loose and fall out].

Acooperator,

Yes indeed! "Work out" as used above, means "figure out", "try to make sense of" or "try to understand".

Of course, as you can see, many others have come up with other meanings.

An additional meaning not mentioned above relates to formulating or developing something as in:

"We really need to work a plan of action, if we are to succeed".

And yet another rather different meaning relates to reconciling differences, becoming friends again after a dispute, as in: "I'm relieved to hear they worked things out".

Or you could simply say:
"I'm so pleased to hear that they worked out their personal differences."