How to use nodal analysis in resistive circuits
In Nodal analysis (KCL),

Kirchhoff's Current Law implies that the sum of currents going in equal to the sum of currents going out. $$\Sigma_{k=1}^n {I}_{in} = I_{out}$$

A.) So you have two ways of going at it either


assume all currents are going in to a node. Then construct an equation in which that the the addition of all currents is equal to  zero
intuitively decide in each branch if the current is going out, or going in. Then construct an equation where the left-hand side is the addition of currents going into the node, and right-hand side is the addition of the currents going out (or vice-versa)


B.) There exists a useful equation for each node in which more than two branches meet. So in this case there is 1 good equations. For each node i'd recommend assigning a variable (like Va for the one between all resistors)

We subtract the voltage at the tail of the direction of current to that of the head it would be as follows

(going into node)
$$I_{1} = (30-Va)/8$$
(going out of node) 
$$I_{2} = Va/3$$  (going out of node)
$$I_{3} = Va/6$$
note: current subscript correspond to resistor subscript
$$I_{1} = I_{2} + I_{3}$$
$$(30-Va)/8 = Va/3  + Va/6$$

Simplify this and you notice Va = 6, thus the book answers are correct.