Explanation:

Let's find the minimum value of the expression \(6 - 4 \sin \theta\) when \(0 \leq \theta \leq \pi/2\).

- Sine Function Behavior:

- In this range, \( \sin \theta \) varies from 0 to 1.

- Minimum value for \(\sin \theta\) is 0, and maximum is 1.

- Substituting in the Expression:

- When \(\sin \theta = 0\), the value of the expression is \(6 - 4 \times 0 = 6\).

- When \(\sin \theta = 1\), the value is \(6 - 4 \times 1 = 2\).

- Answer Analysis:

- So, the expression reaches its minimum value of 2 when \(\sin \theta = 1\).

Based on this analysis, the correct option is Option 2: 2.