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!