My first thought would be to draw a diagram.

The problem says the oil well is 4 km offshore. I assume that's the shortest distance, so a vector from the refinery to the "nearest point" would form a right angle with the short. I assume you know why? Suppose it formed some other angle, then what?

Most shorelines are not straight lines, but I think you're supposed to assume that this one is. That means we have a right triangle, 4 km one side, 11 km another, and then the hypotenuse. How long is that? How much would it cost to build a pipeline along the hypotenuse? Probably not the lowest cost. Now suppose you built the pipeline 4 km + 11 km, maximum distance on land. How much would that cost? And finally, what if you picked an intermediate point?