One number is four less than a second number. Three times the first is 13 more than 4 times the second. Find the numbers.

Let first number is x
second number be y

one number is four less than a second number: x=y-4

Three times the first is 6 more than 6 times the second: 3x=6y+6

substitute x=y-4 in 3x=6y+6

3x =6y+6
3(y-4)=6y+6

3y-12=6y+6

3y-6y=6+12
-3y=18
y=-6

substitute y=-6 in x=y-4

x=-6-4=-10

so first number is -10
second number is -6