Make you best attempt at coming up with the node equation for node e. We then have something to look at that gives us an idea of how you are thinking and what you are missing.
We won't just show you how to do it -- that won't help you. You've seen examples worked, probably on several occasions. Something hasn't clicked and seeing yet one more example worked by someone else is unlikely to change that. You need to struggle through the problem with minimal assistance in order to get that something to finally click.
It appears that you have studied the theory of node equations; however, what you really need is a method for actually writing the node equations. (I follow the same procedure every time, which leads to making fewer errors.)
1. Identify the nodes with unknown voltage, then color-code & label them on the diagram.
2. If a ground node has not been identified, then choose a node to be the ground reference.
3. Write the node equations: add the currents flowing at each of the nodes & set it equal to zero. The general form for a current is: (Voltage@node - Voltage@adjacent node)/(Resistance to adjacent node). If the current is from a current source, current leaving the node is positive.
4. If there are dependent sources, find a way to relate the dependency to the node voltages. Annotate this on the diagram.
5. Solve the node equations.
the schematic is somewhat tricky ... it's about the (actual) polarity of your voltage sources ...
,.. if the author was an idiot - then you have a "non expected" answer appearing to be the "right" one
anyway the multiplication with minus one --e.g.-- a "sign error" -- is likely one of the most common mistakes -- so you can do the both versions and check out if the author went wrong in his mind