Given the translation:
(x, y) ==> (x - 3, y - 4)
(x - 3) ==> This means there was a horizontal shift of 3 to the left
(y - 4) ==> This means there was a vertical shift of 4 units down
From the image given, the correct graph is the third graph.
From the figure above, we can see there was a shift of 3 units left and 4 units down on the graph.