Final answer:
The sentence is a compound-complex sentence as it contains two main clauses and one subordinate clause.
Step-by-step explanation:
The sentence 'During World War I, President Woodrow Wilson kept sheep on the White House lawn and raised money for the Red Cross through the sale of their wool' is a compound-complex sentence. It contains two main clauses ('During World War I, President Woodrow Wilson kept sheep on the White House lawn' and 'raised money for the Red Cross through the sale of their wool') and one subordinate clause ('and raised money for the Red Cross through the sale of their wool').