Find the values of m and n, in each case, If:
`(-6, n+2)` on reflection in origin gives `(m+3, -4)`

Answer

To solve the problem, we need to find the values of \( m \) and \( n \) given the reflection of the point \((-6, n+2)\) in the origin results in the point \((m+3, -4)\).

### Step-by-step Solution:

1. **Understanding Reflection in Origin**:
When a point \((x, y)\) is reflected in the origin, its coordinates change to \((-x, -y)\).

2. **Applying Reflection to the Given Point**:
For the point \((-6, n+2)\):
- The x-coordinate after reflection will be \(-(-6) = 6\).
- The y-coordinate after reflection will be \(- (n + 2) = -n - 2\).
Therefore, the reflected point is \((6, -n - 2)\).

3. **Setting Up the Equation**:
We know that this reflected point \((6, -n - 2)\) is equal to the point \((m + 3, -4)\). Hence, we can set up the following equations:
- \( m + 3 = 6 \)
- \( -n - 2 = -4 \)

4. **Solving for \( m \)**:
From the first equation:
\[ m + 3 = 6 \]
Subtracting 3 from both sides:
\[ m = 6 - 3 = 3 \]

5. **Solving for \( n \)**:
From the second equation:
\[ -n - 2 = -4 \]
Adding 2 to both sides:
\[ -n = -4 + 2 \]
Simplifying:
\[ -n = -2 \]
Multiplying both sides by -1:
\[ n = 2 \]

6. **Final Values**:
Thus, the values of \( m \) and \( n \) are:
\[ m = 3, \quad n = 2 \]

### Summary:
The values are \( m = 3 \) and \( n = 2 \).