“What would you say is your greatest strength, and what's your greatest weakness?”

You're interviewing a candidate for a job. You want to know what he is good at and what problems he might cause if you hire him. You ask:

What would you say is your greatest strength, and what's your greatest weakness?

What would you say (question)?

This is a style of question that people use mostly in interviews. Asking a question like this will make the listener answer more slowly and carefully:

What would you say was the best part about working there?

What would you say is your favorite film of the last 10 years?

There can also be questions of this type that start with different question words:

Who would you say is the strongest member of your team?

You might also see questions like these on written surveys.

your greatest strength

In interviews, people often ask about a person's "greatest strength". Your "greatest strength" is the one thing that you're best at, or your best personality trait. 

Here are some examples of answers:

My greatest strength is my patience.

I'd say that my greatest strength is my willingness to take risks.

strength/weakness

"Strength" and "weakness" are opposites. These words are also used together a lot:

Make a list of your strengths and weaknesses.

You should focus on your strenths, not your weaknesses.