Multiply by the conversion factors that cancel the units you have and give you the units you want.
[tex]1200\dfrac{g}{L}\times\dfrac{1\,L}{1000\,mL}\times\dfrac{100\,cg}{1\,g}=\dfrac{1200\cdot 100\,cg}{1000\,mL}\\\\=\bf{120\dfrac{cg}{mL}}[/tex]
Your best choice is ...
... B. 120 cg/mL
