Find the values of I₁, I₂ and I.

Dear student,

The two resistor are connected in parallel connection. The potential difference across each other are same.
The current through resistor of 3 $\Omega$ is,
$I_1=\frac{V}{R}=\frac{3}{3}=1A$
The current  across resistor of 6 $\Omega$ is 
$I_2=\frac{3}{6}=0.5A$
The total current in circuit is
$$\begin{gathered} I=I_1+I_2 \\ I=1+0.5 \\ I=1.5A \end{gathered}$$

Regards.