Your solution: For perimeter of small square, it is 16x4=64cm, but this is only for 1 small square and you have 4 of them.

Also, you cannot just subtract the perimeter of small squares from perimeter of big square.

Observe the diagram I drew. The new perimeter you are required to find is the pink highlighted one.

For every small square cut out, you need to include 2x (length of side of small square).

So 68cm is the longer length of the new diagram and 16cm is the shorter length of the new diagram.
Hope this helps. :)