Answer
There is no point off the axis (other than infinity) at which the net force on the third particle would be zero.
Work Step by Step
The gravitational force on the third particle due to the particle of mass $m$ is directed toward the particle of mass $m$.
The gravitational force on the third particle due to the particle of mass $2m$ is directed toward the particle of mass $2m$.
For the net gravitational force on the third particle to be 0, the two gravitational forces must point in opposite directions.
Therefore, there is no point off the axis (other than infinity) at which the net force on the third particle would be zero.
