Given bode plot, determine the poles and zeroes
First, consider that zeros are values where the numerator of a transfer function equal zero. Poles are values where the denominator of a transfer function equals zero. When the numerator is zero, the output is zero. When the denominator is zero, the output shoots up to infinity, and in the case of a filter, in unstable.
Now a pole zero plot in 3D will look like this:

This plot is in the complex plane. The frequency response plot can be obtained by taking the magnitude along the imaginary axis. This plot is double sided, but we only care about the positive half most of the time.
In the case of the frequency response plot you posted, I see three zeroes and two poles.  You are correct that \$H(j20)=0\$. By the the definition of a zero, that means that is a zero. I'm not going to give you any more answers until you show some effort.