To find the distance between the points \((-1, 2)\) and \((3, 4)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (-1, 2)\) and \((x_2, y_2) = (3, 4)\).
Now, we can plug in the values:
\[ d = \sqrt{(3 - (-1))^2 + (4 - 2)^2} \]
Calculating the differences:
\[ d = \sqrt{(3 + 1)^2 + (4 - 2)^2} = \sqrt{(4)^2 + (2)^2} \]
Now, square the differences:
\[ d = \sqrt{16 + 4} = \sqrt{20} \]
Now, simplify \(\sqrt{20}\):
\[ \sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5} \]
Thus, the distance between the points \((-1, 2)\) and \((3, 4)\) is:
\[ \boxed{2\sqrt{5}} \]