Help please? My teacher did an easy momentum problem but I don't know where the numbers come from.?

From what you've written, I think you know that the initial total momentum is 13mv/9. Now let the final velocity of the combined m be y units. The combined m is 4m+m=5m so 13mv/9=5my which gives y as 13v/45. This is the CORRECT ANSWER regardless of what ur teacher said.