To find the length of side \( \overline{YZ} \), we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
We have the coordinates of the points \( Y(-4, 6) \) and \( Z(-2, 2) \).
Substituting these coordinates into the distance formula, we get:
\[ d_{YZ} = \sqrt{((-2) - (-4))^2 + (2 - 6)^2} \]
Now, calculate the differences:
\[ (-2) - (-4) = -2 + 4 = 2 \]
\[ 2 - 6 = -4 \]
Substituting these values back into the formula gives:
\[ d_{YZ} = \sqrt{(2)^2 + (-4)^2} \]
Calculating the squares:
\[ d_{YZ} = \sqrt{4 + 16} = \sqrt{20} \]
Now, simplify \( \sqrt{20} \):
\[ d_{YZ} = \sqrt{4 \cdot 5} = 2\sqrt{5} \]
To find the approximate value of \( 2\sqrt{5} \):
Using \( \sqrt{5} \approx 2.236 \):
\[ d_{YZ} \approx 2 \cdot 2.236 \approx 4.472 \]
Rounding this to one decimal place:
\[ d_{YZ} \approx 4.5 \]
Thus, the length of side \( \overline{YZ} \) is approximately \( \boxed{4.5} \).