Let x be the daughter's age.
Set out two sentences that are true for this year.
First statement tells us that a year ago, mother was 4 times daughter's age. The daughter would have been x-1 at that point, so mother would be 4(x-1). Now it's a year later, so mother is 4(x-1) + 1.
Second statement says that in three years, mother will be 3 times daughter's age. Daughter will be (x+3) then, so mother will be 3(x+3). That's still three years in the future, so now, mother is 3(x+3)-3.
Two different ways of finding mother's age this year, so you can set them equal to each other.
4(x-1) + 1 = 3(x+3) -3
Multiply out brackets.
4x - 4 + 1 = 3x + 9 -3
Simplify
4x -3 = 3x + 6
subtract 3x from both sides
x - 3 = 6
add 3 to both sides.
x = 9.
Daughter is now nine. A year ago, she was 8, and mother was therefore 32. So mother is now 33. In three years, daughter will be 12, and mother will be 36.