We have to sent $1200\;\text{bytes}$ out of which $20$ bytes is header. So, a tual data to be transmitted $=1180$ bytes.
Each fragment can have $100\;\text{bytes}$ data and $20\;\text{bytes}$ header as MTU is $100+20=120\;\text{bytes}$. But, the payload must be a multiple of $8$ as the offset field uses multiple of $8$ as it's unit. This means the router can only sent $96$ bytes of data in a fragment.
So, to send $1200\; \text{bytes}$ the router needs $\left\lceil \dfrac{1200-20}{96}\right \rceil=13$ fragments.