With the current, you can canoe 96 miles in 4 hours. Against the same current, you can canoe only $\frac{3}{4}$ of this distance in 6 hours. Find your rate in still water and the rate of the current.

Step 1 ：Let's denote the rate of the canoe in still water as 'c' and the rate of the current as 'r'.

Step 2 ：From the problem, we know that with the current, the canoe can travel 96 miles in 4 hours. This gives us the equation \(c + r = \frac{96}{4} = 24\) miles per hour.

Step 3 ：Also, against the current, the canoe can travel only \(\frac{3}{4}\) of the distance (72 miles) in 6 hours. This gives us the equation \(c - r = \frac{72}{6} = 12\) miles per hour.

Step 4 ：Solving these two equations simultaneously, we find that \(c = 18\) and \(r = 6\).

Step 5 ：So, the rate of the canoe in still water is \(\boxed{18}\) miles per hour and the rate of the current is \(\boxed{6}\) miles per hour.