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. :)

Alternatively, you can observe that every small square cut out, actually the new pink highlighted lengths are the green highlighted ones, which is from the uncut square.

Hence, cut and uncut square, their perimeters are actually the same since the green highlighted ones = pink highlighted ones.