Juan aims his boat directly across a river flowing at 8mi/hr. juan's boat travels at 6 miles/hr in still water. how was does juan travel relative to shore

6mph:

Suppose the boat is traveling on a y axis. The river flow acts on the x axis. Motion on each axes are independent. The linear speed of the boat is not changed. Furthermore the projectile motion is changing, but you're specifically asking about the linear speed of the boat which is unchanged.