For such questions that start with both persons having an equal number of something, change the denominator to be the same.
Eve gave away : 4/5 = 16/20
1 - 16/20 = 20/20 - 16/20 = 4/20
So Eve had 20 units of roses at first. She gave 16 units away and had 4 units left.

Mary gave away : ¾ = 15/20
1 - 15/20 = 20/20 - 15/20 = 5/20
So Mary had 20 units of roses at first. She gave 15 units away and had 5 units left.

As you can see both had a equal number of units of roses at first.
5 units - 4 units = 1 unit
In the end, Mary has 1 unit more roses than Eve.
So 1 unit = 3 since Mary had 3 roses more than Eve in the end.

Roses that Eve had at first = 20 units
= 20 x 3 = 60