A standard technique to do this question is as follows.

(1) The denominator contains 4 and 3, so we try to make the number of units of stickers at first be multiples of 4 and 3. Make sure you take note of this multiple because it makes things simpler.

(2) Let the number of stickers at first be 12 units, because 12 is a multiple of 4 and also a multiple of 3.

(3) There would be 6 units of red stickers and 6 units of blue stickers at first since there is an equal number of each of them.

(4) Giving away 2/3 of her 6 units of red stickers means she gives away 4 units of red stickers, leaving behind 2 units of red stickers.

(5) Now, she gives away some blue stickers also, but how many?

(6) Because she has 1/4 of her original 12 units of stickers, she has a total of 3 units of stickers at the end. But remember from (4) that she has 2 units of red stickers at the end.

(7) This means that she has only 1 unit of blue stickers at the end. But remember from (3) that she started out with 6 units of blue stickers.

(8) She gave away 5 units of blue stickers.

(9) So she gave away 5 units of blue stickers out of her original 6 units of blue stickers, so the relevant fraction is 5/6.

Mandy, I do not recommend writing the question down in ratio form. Units are often easier.

Also, always do a “before and after” analysis like now I did in my explanations.