If $V_A=96\mathrm{.}2$hat$(i)$ in $\frac{?}{sec}$ in the figure below, find ${}_2,$ the angular speed of bar $B_2.$

To calculate the angular speeds of the two bars $B_2$ and $B_3,$ you need to use the two point formula:

first on rigid body $B_2$ to calculate the velocity of point $B($since you know velocity at point $A)$

then on rigid body $B_3$ to calculate the velocity of point $D($since you know velocity at point $B)$

Note that the velocity at point $D$ has to be zero. Thus the two components of the velocity are zero giving you two equations to solve for the two unknown angular velocities.