At the end of The Picture of Dorian Gray, Henry burns both Dorian and the painting, but later on he sees the painting of Dorian in his home?

Your question is a perfect reason why students should never substitute a movie for a work of literature! The writers of screen plays and directors themselves change things in order to increase the viewing of their movie.  This is definitely reflected in your question.  Why?  The details of the original work, The Picture of Dorian Gray, and the details of the movie you provide differ greatly.  Let's look at each in turn.

First, let's look at the actual story, The Picture of Dorian Gray, along with its original ending.  In short, the picture is revealed.  The picture is grotesque, featuring blood dripping form a knife.  This is all we see, in reality because it is a "crash" that is heard from the servants in other parts of the household.  The next thing we are shown, as readers, is the original picture of Dorian Gray looking young and vibrant.  In opposition, there is a shriveled, decrepit old man on the floor.  He is dead and with a knife plunged into his heart.  There is an effort made to identify the man.  The only evidence that it is truly Dorian Gray is the rings that remain on his fingers.  (Please note, neither Dorian NOR the picture is burned in the real story!  In the original written work, there is no "later on" for him to see the painting in the future!)

Behind every exquisite thing that existed, there was something tragic.

Next, let's look at the movie that came out a few years ago.  It is not called The Picture of Dorian Gray, but is distinguished from the original work by being called simply Dorian Gray. This change in title is appropriate because the ending is VASTLY different!  This is the ending you refer to.  More appropriately, it is the climax that is changed.  In this version, Dorian Gray IS burned.  The painting is burned as well.  The stabbing happens only after Gray is faced with lethal fire.  Then the resolution of the movie does show Henry traversing the attic and finding the painting.  However, this is NOT what happens in the book!

In conclusion, it's important to note one similarity:  the painting is stabbed.  That is where the similarities end.  Further, your quesiton is a very important one in that it should prove to students that reading the actual book is more important than watching a theatrical version.