The demand function is $\displaystyle p=\frac{-5}{2}Q + b_1$. I assume you are ok to this point.
Any point can be substituted into this equation to find $\displaystyle b_1$.
They have chosen the point where p=10 and Q=32.
This gives:
$\displaystyle 10 = \frac{-5}{2}* 32 +b_1$
$\displaystyle 10 = -80 + b_1$
$\displaystyle b_1 = 90 $
Similarly for the supply function.