Hey there! 
P₄ + Cl₂ → PCl₃ 
First, let's balance Cl. 
There are 2 on the left, and 3 on the right. 
To balance this, let's put a coefficient of 3 in front of Cl₂ and a coefficient of 2 in front of PCl₃. 
P₄ + 3Cl₂ → 2PCl₃ 
Now we have 6 on the left and 6 on the right. 
Next, let's balance P. 
There are 4 on the left and 2 on the right. 
Let's change the coefficient in front of PCl₃ from 2 to 4. 
P₄ + 3Cl₂ → 4PCl₃ 
There are now 4 P on each side. 
However, now Cl is unbalanced, with 6 on the left and 12 on the right. 
We can change the coefficient in front of Cl₂ from 3 to 6. 
P₄ + 6Cl₂ → 4PCl₃ 
So now, we have 4 P on each side and 12 C on each side. 
This is our final balanced equation. 
Hope this helps!