The correct option is A in order that
The options are compound conjunctions, they're phrases that link clauses or sentences together. In the sentence, the person speaks loudly with the purpose that all should hear. From the options. "in order that" means 'for the reason'. It expresses purpose in a sentence, hence option A is correct. "On condition that" is used to express a condition based on which an action takes place, it does not apply to the sentence as the sentence changes its meaning to 'If all might hear, then will she speak loudly', which is the opposite of what the original sentence means. Hence option B is incorrect. Similarly, "provided that" means 'on provision on', it refers to the condition if fulfilled, will the person speak loudly, and the sentence is not condition-related, hence option D is incorrect. "Even if" expresses a hypothesis, it refers to an unreal or imaginary situation. When placed in the sentence it doesn't sound complete, because the sentence does not state an imaginary situation, but the purpose for her speaking loudly, hence option C is incorrect.