Answer
The current through $R_{4}$, $R_{5}$ and $R_{6}$ is $\frac{10}{99}$ $amperes$ each or $0.0621$ $A$.
Work Step by Step
Please use the attached diagram for the calculation of $R_{eq}$:
$R_{2}$ and $R_{3}$ in parallel:
$R_{23}$ $=$ $\frac{40\times10}{40+10}$ $=$ $8$ $ohms$
$R_{4}$, $R_{5}$ and $R_{6}$ in parallel:
$R_{456}$ $=$ $\frac{15}{3}$ $=$ $5$ $ohms$
(Note: For parallel resistors with equal value, the equivalent resistance is the value divide by the number of equal resistors.)
$R_{1}$, $R_{23}$ and $R_{456}$ in series:
$R_{eq}$ $=$ $20 + 8 +5$ $=$ $33$ $ohms$
Total circuit current $I$ is:
$I$ $=$ $\frac{V_{s}}{R_{eq}}$ $=$ $\frac{10}{33}$ $amperes$
Using KCL:
$I- I_{23} - I_{456} = 0$
By Current Divider, we can determine $I_{23}$ and $I_{456}$ respectively,
$I_{23}$ $=$ $I\times\frac{R_{456}}{R_{23}+R_{456}}$ $=$ $\frac{10}{33}\times\frac{5}{8+5}$ $=$ $0.1166$ $A$
$I_{456}$ $=$ $I\times\frac{R_{23}}{R_{23}+R_{456}}$ $=$ $\frac{10}{33}\times\frac{8}{8+5}$ $=$ $0.1864$ $A$
Now since $R_{4}$, $R_{5}$ and $R_{6}$ have equal values:
$I_{4}$ $=$ $I_{5}$ $=$ $I_{6}$ $=$ $\frac{I_{456}}{3}$ $=$ $\frac{0.1864}{3}$ $=$ $0.0621$ $amperes$
