In 1 meter, there are [tex]10^9[/tex] nanometers, and in 1 second there are [tex]10^{12}[/tex] picoseconds, so we have
[tex]\dfrac{3.0\times10^8\text{ m}}{1\text{ s}}\cdot\dfrac{10^9\text{ nm}}{1\text{ m}}\cdot\dfrac{1\text{ s}}{10^{12}\text{ ps}}=3.0\times10^{8+9-12}=3.0\times10^5\dfrac{\text{nm}}{\text{ps}}[/tex]
