Suganya writes . . . . . . . . her left hand.

The correct answer is Option B: with.

The preposition "with" is used to indicate the instrument or means by which an action is performed. In this case, the sentence suggests that Suganya is using her left hand to write. Therefore, we use the preposition "with" to express the idea of using a particular body part as a means for writing.

The other options are not suitable in this context:
Option A: "on" is used to indicate a surface or location, but it does not convey the idea of using the hand for writing.
Option C: "in" indicates being inside or within something, which does not fit the context of writing with a hand.
Option D: "by" can indicate agency or means, but it is not as appropriate as "with" in this specific sentence.

Overall, the most appropriate preposition to complete the sentence is "with" as it conveys the intended meaning that Suganya writes using her left hand.