Can someone break this question down in a simpler form to where I can undersrand it. What am I being asked to do this is for social work?

You are asked to give two different approaches to designing a particular research study, specifically  a qualitative approach and a quantitative approach.  The goal of each study is to evaluate the success of a particular program.    That program will use in-home social services rather than out-of-home placements (foster or group home placements, typically) in situations where children are at risk of being abused.

Then, you're asked to compare and contrast those twp approaches, and to discuss whether combining both approaches is desirable.

Typically, a quantitative approach is used to test a theory.  You use statistical methods to determine how well predictions made by the theory match measured real-world results. 

A qualitative study attempts to identify and understand a problem, without regard to any existing theory and perhaps to develop a new theory. 

That's a very rough breakdown of what you're asked to do. 

For a more detailed discussion, specifically from a social sciences point of view, you might want to read:

https://sites.uci.edu/socscihonors/files/2017/09/Q...

If you have more questions along this line, there's a whole category for "Social Science".  Placing your question there rather than letting a Yahoo! algorithm pick a category for you, is likely to get you better and quicker results.  (Your question ended up in "Programming & Design", probably because of the the word "program" in the question.  It's not a very smart algorithm, is it?)

I think that is like pros and cons of a child being in a good home or bad.

I think it’s saying “Pros and cons of qualitative and quantitative research into how successful prevention schemes of child abuse in foster children are. 

Qualitative - long answers with options from the families and social workers. 

Quantitative - short yes/no questions, surveys, limited chat with actual people.