The smaller number is 3 more than the larger. four times the larger is the same as 13 minus six times smaller

We will say the smaller number is X and the larger number is Y
The first sentence states y=x+3 and the second sentence states 4y=6x-13
You can use substitution in this to plug in y=x+3 into 4y=6x-13 to get
4(x+3)=6x-13 now move -13 to the other side to get 4x+16=6x then move 4x to the other side to get 16=2x giving you X
X=8
Now plug in X into the equation y=x+3
y=(8)+3 giving you Y
Y=11
Now plug in both X and Y to check
4(11)=6(8)-13
44=35