The clue set here is cough, coughing up blood, kidney inflammation, and a positive c-ANCA test. The antibody type is the fastest way to sort the vasculitis options.
Since the antibody is c-ANCA and the organs hit are lungs and kidneys, the disease that matches on both counts is Wegener's granulomatosis.
Let's summarize:
The correct answer is Wegener's granulomatosis.