How can I determine the order of filter?
Note that the given slopes of $6n\textrm{ dB}/\textrm{octave}$ and $20n\textrm{ dB}/\textrm{dec}$, respectively, are asymptotic slopes for large frequencies. So you have to extrapolate the lines that are approximated by the magnitude responses at large frequencies.

For the given figure you could do the following. For the second order filter, look at the attenuations at $f=10^2\textrm{Hz}$ and at the next vertical line, which corresponds to $f=2\cdot 10^2\textrm{Hz}$. The ratio between those two frequencies is an octave, and the difference in attenuation is approximately $-22-(-35)\textrm{dB}=13\textrm{dB}$ (should be $12\textrm{dB}$).

For the $12^{th}$order system you could look at the attenuation values at $30\textrm{Hz}$ and $40\textrm{Hz}$, taking into account that the curve flattens towards its knee, and you need to extrapolate the straight line. With this in mind you would arrive at approximately $-31\textrm{dB}$ at $f=40\textrm{Hz}$, and at $-2\textrm{dB}$ at $f=30\textrm{Hz}$, which corresponds to a difference of $29\textrm{dB}$. Solving

$$\left(\frac{4}{3}\right)^x=2\tag{1}$$

for $x$ gives $x\approx 2.41$, i.e., you have to multiply $29\textrm{dB}$ with $2.41$ to obtain the attenuation per octave: $29\cdot 2.41=69.9\textrm{dB}$ (should be $72\textrm{dB}$).