Let's balance step by step. We'll start with Iron (Fe)
Fe2O3 + HCl --> FeCl3 + H2O
We have 2 Fe on the left, and only one on the right, so we'll double the Fe on the right
Fe2O3 + HCl --> 2FeCl3 + H2O
Now we have six Cl on the right, and only one on the left, so we'll multiply the Cl by six on the left
Fe2O3 + 6HCl --> 2FeCl3 + H2O
Finally, we can balance the water, as we have 6 H and 3 O on the left, and 2 H and one O on the right, so we can triple the H2O on the right
Fe2O3 + 6HCl --> 2FeCl3 + 3H2O
The equation has been balanced.
