Option 1 -> "had been reported how" is grammatically incorrect; "report" doesn't work with this structure.
Option 2 -> "had been exclaimed how" doesn't work; "exclaim" is not used in passive voice this way.
Option 3 -> "had been taught how" is grammatically correct and makes logical sense with the passive construction.
Option 4 -> "had been inferred how" is incorrect; you don't "infer someone how something works."
Hence, Option 3: taught -> The sentence requires a verb that works in passive voice ("had been + past participle") and can be followed by "how it worked." "Taught" perfectly fits this structure, meaning they received instruction about how something worked on multiple occasions -> correct