Statement I The equation `|(x-2)+a|=4` can have four distinct real solutions for x if a belongs to the interval `(-oo, 4)`.
Statemment II The number of point of intersection of the curve represent the solution of the equation.
(a)Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I
(b)Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement I
(c)Statement I is correct but Statement II is incorrect
(d)Statement II is correct but Statement I is incorrect

Options

A. Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I
B. Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement I
C. Statement I is correct but Statement II is incorrect
D. Statement II is correct but Statement I is incorrect

Answer

To solve the problem, we will analyze both statements step by step.

### Step 1: Analyze Statement I
The equation given is \( |(x - 2) + a| = 4 \).

1. **Break down the absolute value**:
The absolute value equation can be split into two cases:
\[ (x - 2) + a = 4 \quad \text{or} \quad (x - 2) + a = -4 \]

2. **Rearranging the equations**:
- From the first case:
\[ x - 2 + a = 4 \implies x = 6 - a \]
- From the second case:
\[ x - 2 + a = -4 \implies x = -2 - a \]

3. **Finding the number of solutions**:
The solutions for \( x \) are:
\[ x = 6 - a \quad \text{and} \quad x = -2 - a \]
For these to be distinct solutions, we need to ensure that these two values are different:
\[ 6 - a \neq -2 - a \]
This simplifies to:
\[ 6 \neq -2 \quad \text{(which is always true)} \]
Therefore, there are always two distinct solutions for any value of \( a \).

4. **Checking the interval for \( a \)**:
The statement claims that there can be four distinct real solutions if \( a \) belongs to the interval \( (-\infty, 4) \). However, as we have shown, there can only be two solutions regardless of the value of \( a \). Thus, **Statement I is incorrect**.

### Step 2: Analyze Statement II
Statement II claims that the number of points of intersection of the curve represents the solution of the equation.

1. **Understanding the intersection**:
The solutions to the equation \( |(x - 2) + a| = 4 \) can be interpreted graphically as the points where the line \( y = (x - 2) + a \) intersects the horizontal lines \( y = 4 \) and \( y = -4 \).

2. **Conclusion about intersections**:
Since the number of intersection points corresponds to the number of solutions to the equation, **Statement II is correct**.

### Final Conclusion
- **Statement I** is incorrect because the equation cannot have four distinct solutions for any value of \( a \) in the given interval.
- **Statement II** is correct as it accurately describes the relationship between the number of intersection points and the solutions of the equation.

### Answer
The correct option is (d): Statement II is correct but Statement I is incorrect.