In a parallelogram, the diagonals bisect each other. If one half of a diagonal measures 3x+2 and the corresponding half of the other…

The two expressions are said to be equal, so set them equal: $3x+2=5x-6$. Subtract $3x$ from both sides: $2=2x-6$. Add $6$: $8=2x$, so $x=4$, choice B. Check: $3(4)+2=14$ and $5(4)-6=14$. Choice A ($2$) gives $8$ and $4$. Choice C ($6$) gives $20$ and $24$. Choice D ($8$) gives $26$ and $34$. Only $x=4$ makes the two halves of the diagonals equal in length, as they must be since the diagonals of a parallelogram bisect each other.