Balancing chemical equations is like a small puzzle. The ultimate goal is to end up with the same number of atoms on both sides of the arrow.
To start, check to make sure it isn’t already balanced. If coefficients aren’t present, it’s assumed to be one. In this case, there’s just one aluminum on both sides, but the right hand side has one more fluorine than the left. This means that we’ll have to change the coefficients to make them match. Since we can’t multiply the two fluorines to make three with a whole number, we have to change this one and the one in front of the aluminum fluoride. Let’s put a 3 in front of F2 and a 2 in front of AlF3. So far, we have:
Al + 3F2 -> 2AlF3
Check the number of fluorines; sure enough, we have six on both sides. However, we’ve imbalanced the aluminums by balancing the fluorines. The fix is easy, though; change the coefficient from one to two in front of the aluminum to make them match. The result is therefore:
2Al + 3F2 -> 2AlF3
Check your element totals again; sure enough, they’re all balanced. This is the balanced chemical equation.
Hope this helps!