Elisha shows Jesus-like wisdom here as he helps this family in need.
Their needs needs seem obvious but he doesn't presume to know what to do or how to respond. He is seeking direction from the Lord by asking the wife questions.
Most specifically, it's interesting to me that he asks her what she already has that may help, as opposed to just giving her something that he has or can get.
In addition to that, he asks her to ask for help from her neighbors. His direction is specific and intentionally in calling her own community to become part of the solution. This would have been natural for them to do in that day (and for most cultures except the more individualized western cultures like the US) but not necessarily easy under these shameful circumstances.
My takeaway is, when helping people in need, to ask questions. These questions seem like good ones to have handy whenever someone asks for your help:
How can I help you?
What do you already have that may help?
How might your neighbors or local family help?
What is God saying to you?
What are you going to do about it?