The perimeter \( P \) of a rectangle can be calculated using the formula:
\[ P = 2 \times ( \text{length} + \text{width} ) \]
In this case, the perimeter is given as 22 inches, and the width is 6 inches. We can denote the height (or length) as \( h \). Plugging in the known values, we get:
\[ 22 = 2 \times (h + 6) \]
Now, we can simplify and solve for \( h \):
- Divide both sides of the equation by 2:
\[ 11 = h + 6 \]
- Subtract 6 from both sides:
\[ h = 11 - 6 \] \[ h = 5 \]
Therefore, the height of the postcard is 5 inches.