The number of chickens to the number of ducks on a farm was 6:5. After 63 ducks were sold, there were 3 times as many chickens as ducks left.

I found this question a bit confusing too

We are told two things so we will need to set up 2 equations and solve them simultaneously.

$$\\\frac{6}{5}=\frac{C}{D}\qquad \rightarrow \quad C=\frac{6D}{5}\qquad \qquad \qquad (1)\\\\

\frac{3}{1}=\frac{C}{D-63}\quad \rightarrow \quad C=3(D-63)\qquad (2)\\\\$$

so

$$\begin{array}{rll}

\frac{6D}{5}&=&3(D-63)}\\\\

\frac{2D}{5}&=&1(D-63)}\\\\

2D&=&5(D-63)}\\\\

2D&=&5D-315\\\\

315&=&3D\\\\

D&=&105 \qquad \mbox{There were originally 105 ducks}\\\\\\

C&=&6*105\div 5\\\\

C&=&126 \qquad \mbox{There were originally 126 chickens}\\\\\\

\end{array}$$

$${\mathtt{105}}{\mathtt{\,\small\textbf+\,}}{\mathtt{126}}{\mathtt{\,-\,}}{\mathtt{63}} = {\mathtt{168}}$$

In the end there were 168 birds.

I did check that all these numbers make the original described situation true and you should do that too :)