She will have five pieces of chains after the 2 cuts. The chains will have loops of 1, 1, 3, 6 and 12.

The chain is made up of interlocking loops. So when you make 1 cut in the chain in the middle, you would end up with 2 chains and 1 cut loop. So 2 cuts in the middle would leave you with 3 chains and 2 cut single loops.

So the jeweler makes one cut on the 4th loop making a 1 cut loop, a 3 loop chain, and a 19 loop chain. Then a cut on the 7th loop of the 19 loop chain leaving a 1 cut loop, a 6 loop chain, and a 12 loop chain. So at the end she has 1 cut loop, another 1 cut loop, a 3 loop chain, a 6 loop chain, and a 12 loop chain.