Arrange the 4 pieces into a big slitherlink.
To help you arrange it, First find the solvable small slitherlink then put it in the bottom-left position.
The big slitherlink looks like this:
The first piece can not be on the bottom because a link has to leave to the bottom between the 2 and the 1. The second piece can not be on the right because either the 3s in the top right or the 3 in the bottom right will cause a contradiction. Next I tried the pieces 1, 3 and 4 in the top left (this would force the second piece into the bottom left) and found contradictions. This leaves the second piece in the top left and the first piece in the top right. The fourth piece can not be to the right of the third piece because the 3s there yield a contradiction. This leaves us with the order 2-1-4-3. The resulting big slitherlink can be solved fairly straightforward.