Step 1: Read the clinical picture. A young, allergic, asthmatic woman with nasal polyps, thick mucosal disease and impacted secretions points toward allergic fungal rhinosinusitis.
Step 2: The decisive clue is the microscopy: septate hyphae that branch dichotomously (into two equal branches) at acute angles of about 45 degrees. This is the classic morphology of Aspergillus. So option B is correct.
Step 3: Option A is wrong. Rhizopus is a Mucorale. Its hyphae are broad, ribbon-like and aseptate (or sparsely septate) and branch at wide, roughly 90 degree angles.
Step 4: Option C is wrong. Mucor is also a Mucorale with the same broad, aseptate, wide-angle hyphae and typically causes invasive rhino-orbital disease in diabetics, not allergic polyposis.
Step 5: Option D is wrong. Candida shows budding yeasts with pseudohyphae, not regular acute-angle dichotomous branching, and it does not cause this allergic fungal sinusitis picture.
Conclusion: Septate, acute-angle (45 degree) dichotomously branching hyphae in an allergic patient mean Aspergillus. Answer: option B.