Removing a beam can brighten one point

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Problem: Removing a beam can brighten one point
Two coherent beams separately give 16 and 4 W/m² at a detector. They arrive exactly out of phase. The weaker beam is then blocked without changing the stronger beam.
Question: By how much does the detector intensity increase?
Givens:
- I₁ = 16 W/m²
- I₂ = 4 W/m²
- Initial phase difference = 180°
Assumptions: Same-frequency coherent beams, parallel polarization, same observation medium and unchanged individual detector intensities, unless the prompt explicitly averages phase.
Choices (LaTeX):
A. 12\ \mathrm{W/m^2}
B. 4\ \mathrm{W/m^2}
C. -4\ \mathrm{W/m^2}
D. 20\ \mathrm{W/m^2}

Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.