I think the first or the second phrase works the best
The correct answer is A. Major Tallmadge developed a unique code system so that the Americans could send secret messages.
Explanation:
To find the central idea in a text, ask yourself what is the main idea the author expresses?. For example, in the passage presented the author focuses on the system Major Tallmadge created and how this system was very elaborated or complex, which is shown through details such as "He substituted digits for words" or "Tallmadge gave his agents a cipher". Moreover, the author implicitly suggests this was used for Americans to send secret messages as he mentions important American military leaders such as "Woodhull, Townsend, and General Washington" and shows how important was that the messages were only understood by few. In this context, the main idea is "Major Tallmadge developed a unique code system so that the Americans could send secret messages".
True when labeling the part of speech...hope I helped