Explanation:

To solve the problem of finding a number where the number minus its square root equals 2, we follow these steps:

- Let the number be \( x \).

- The equation becomes: \( x - \sqrt{x} = 2 \).

- Rearrange to find: \( \sqrt{x} = x - 2 \).

- Square both sides to get rid of the square root: \( x = (x - 2)^2 \).

- Expand the equation: \( x = x^2 - 4x + 4 \).

- Rearrange to standard quadratic form: \( x^2 - 5x + 4 = 0 \).

- Solve using factoring or the quadratic formula: \( (x - 4)(x - 1) = 0 \).

This gives solutions \( x = 4 \) and \( x = 1 \).

- Check both:

- For \( x = 4 \): \( 4 - \sqrt{4} = 4 - 2 = 2 \), which is correct.

- For \( x = 1 \): \( 1 - \sqrt{1} = 1 - 1 = 0 \), which is incorrect.

So, the correct option is Option 4: 4.