The correct option is D that
When a clause depends on another clause for its full meaning, it's the subordinate clause (his voice became hoarse) that depends on the main clause (He had shouted so much). To combine these two, a subordinating conjunction is used. The conjunction we use depends on the subordinate clause. The given subordinate clause is the effect of the person's shouting, hence the sentence is effect-related. When the subordinate clause is the cause or justification, then that sentence is cause-related. 'Because' is used when the clause is the cause of the action in the main clause. Since the given statement is the opposite, the subordinate clause is the effect and not the cause, option A is incorrect. Similarly, 'as' is also used for cause-related statements, hence option C is also incorrect. Some conjunctions work in pairs to provide their full meaning, like 'so...that' is a correlative conjunction which is used for effect-related sentences. Since 'his voice became hoarse' is an effect, 'that' replaces the underlined word 'because', and 'so' is already in the sentence, "shouted so much". Hence option D is correct. 'For' is a coordinating conjunction, more specifically, an Illative conjunction which connects two independent statements, where one of them is inferred from the other. Since the given statements are not both independent, one is dependent on the other, option B is incorrect.