Draw a structure for IIR Filter given H(z)
It would help to apply some specificity to the general equation:

$H(z) = \frac{b_0 + b_1z^{-1}+b_2z^{-2}}{1+a_1z^{-1}+a_2z^{-2}}$

Rearrange into a difference equation, skipping the steps for brevity:

$y[n] = b_0x[n] +b_1x[n-1]+b_2x[n-1]-a_1y[n-1]-a_2y[n-2]$

Does the difference equation form show now that the Direct Form structure is derived purely by inspection?