Basic Theory - finding voltage between two points
Given your comment

fig 213a

Why does Vac = 0? There is no connection between B and D. Connect a voltmeter of any practical input impedance between A and C to measure the voltage, and whatever the voltages were on those terminals due to stray capacitances (not shown in that diagram, so assumed to be zero), it will pull those points together, and move points B and D to whatever voltages are needed to get A and C at the same voltage.

If an infinite input impedance voltmeter was connected between A and C, it would not draw any current, and the voltage would stay at whatever it happened to be, due to charges on the capacitances of those nodes. As they're not shown, and the voltages on them are not given, not enough information is given in the question to determine Vac.

Why does Vad = 0? As above, but change 'c' for 'd'.

fig 213b

Why does Vac = 3v? There is a connection between B and D, they are both connected to the same node. The two grounds are drawn on the same schematic, so can be taken to be connected. That node happens to be 'ground', which means the node that we reference all other voltage measurements to, but it could just be another wire. 

As B and D are at 0v with respect to ground, A is at 12v wrt ground, and B is at 9v wrt ground, so there is 3v difference between them.

Further thoughts

I'm inclined to agree with the various comments that the exercise in the book was badly worded, though I struggle to find a good improvement at the noob level it's intended for.

In questions like this, if something is not mentioned, then you should assume it's negligible. No capacitances to ground are illustrated, so they should be effectively zero, so unable to hold those nodes at any given potential. However, the voltmeter is not described, so you should be able to assume it's an ideal voltmeter, which doesn't load the circuit at all. This will leave the measurement of Vac indeterminate.

If instead the question specified a voltmeter with some input resistance like 10Mohms, or asked for the current that flowed through a resistor of (say) 1Mohm or 1k placed between terminals A and C, then there would be no problem.