Finding potential at a point in a circuit

$$I_1=20/7 A$$ , $$I_2=2/7 A$$ and $$I_3=18/7 A$$

In this circuit can we calculate the value of absolute electric potential (or simply potential) at specific points like B or E or A etc ??
My textbook assumed potential of E as $$0$$ and then calculated potential at B = $$-\frac{30}{7}$$ volts. How can we arbitrarily assume potential at different points, is it allowed (when?) ?

How can we arbitrarily assume potential at different points, is it allowed (when?) ?

Yes we can arbitrarily assign any point as being zero potential because, no matter what point we assign, the potential differences will be the same between points in the circuit and that, in general, is all we care about.

But while it may be arbitrary, there are in fact logical points to assign zero potential to make circuit analysis easier, in particular, node analysis where the objective is to determine node voltages. Note that E (which is electrically the same as F and D) is a common node for all three branch currents I1, I2, I3. You will understand how this makes it easier to solve for the node voltages at A, B and C when you learn node analysis, if you haven't already.

You may ask, why would we want to know the node voltages with reference to the common point E (F or D). A practical application is trouble shooting electric circuits. If you know what the voltages should be at the points, you can connect the black (common) lead of your voltmeter to E (or F or D) and connect the red lead to those points to verify the correct voltages exist.

Hope this helps.

It is actually a fundamental principle in physics, that there is no absolute scale for voltage, i.e. you can set your zero point anywhere and define all other voltages in relation to that. It is the same with energy. The only thing that matters physically is voltage difference.

It is usually a good idea to set V=0 at the lowest voltage point in the system, probably at the lower voltage end of one of the batteries