Alf3 is almost insoluble in anhydrous hf but dissolves if kf is present. passage of bf3 through the resulting solution causes alf3 to can anyone explain the idea behind this?

It's because the product formed with BF3 is more complex which able to decompose AlF3.

AlF3 doesn't dissolve in HF because of the fluorine. It's doesn't allow for coordination due to the hydrogen. However, it will dissolve in KF. If you look at the chemical reaction, it's able to form a salt.

3KF+AlF3−>3KF.AlF3