Determining voltages for a network
What you show is inconsistent with itself.  If we consider the batteries to be perfect voltage sources, then this circuit can't exist.

You are explicitly told the left node is at 10 V.  Since no reference is given, that can only be assumed to be relative to ground.  The left battery adds 3 V to that, putting Va at 13 V.

However, the right battery puts Vb at 6 V.  The middle battery then puts Va at 27 V.

Both can't be right, so this circuit is impossible as you presented it here.

Perhaps the text mentions some assumed internal resistances of the batteries?  If so, you model the batteries as perfect voltage sources in series with their internal resistance.  With some finite resistance in series with the batteries, this circuit is possible.

Either the textbook contains a major mistake, or there is some other implied information about this circuit you're not telling us.