What are your family's strengths, or your strengths?
Here's why:
* "Strengths" is plural: We use "strengths" to refer to multiple positive qualities.
* "Family's" is possessive: We use the possessive form "family's" to show that the strengths belong to the family.
* "Or" allows for two options: The "or" gives the listener the choice to describe either their family's strengths or their own personal strengths.
You could also say:
* What are the strengths of your family?
* What are some strengths that your family possesses?
* What are your personal strengths, or what are the strengths of your family?