The coordinates of the midpoint between the points $(1, 2)$ and $(3, 6)$ are $(2, 4)$.

To determine the midpoint between two points, we utilize the midpoint formula, which is given by

where $(x_1, y_1)$ and $(x_2, y_2)$ represent the coordinates of the two points. In our example, the points are $(1, 2)$ and $(3, 6)$.

First, we calculate the sum of the x-coordinates of the two points:

Next, we divide this sum by $2$ to find the x-coordinate of the midpoint:

Now, we proceed to calculate the sum of the y-coordinates:

We then divide this sum by $2$ to find the y-coordinate of the midpoint:

Thus, the coordinates of the midpoint are $(2, 4)$. This indicates that the point $(2, 4)$ is located exactly halfway between $(1, 2)$ and $(3, 6)$ along a straight line. This midpoint calculation method can be applied to any pair of points, making it an invaluable tool in geometry.