Step 1: Understanding the Preposition Usage:
The correct preposition to use when stating what someone teaches in addition to another subject is "beside." It means alongside or in addition to.
Step 2: Analyzing the Options:
- Across: Incorrect, as "across" suggests a direction, not an addition.
- Besides: Incorrect, as "besides" is often used to mean "apart from" or "in addition to," but it does not fit grammatically in this sentence.
- Beside: The correct preposition, meaning alongside or in addition to. "Shyam teaches Mathematics beside English" means that Shyam teaches both subjects.
- Over: Incorrect, as "over" implies authority or a position above, not addition.
Step 3: Conclusion:
The correct preposition is beside, meaning in addition to or alongside.