Natalie's sister bought 2 * 8 = <<2*8=16>>16 diaries.
So she then had 16 + 8 = <<16+8=24>>24 diaries.
Afterwards, she loses 1/4 * 24 = <<24*1/4=6>>6 diaries.
So, Natalie's sister now has 24 - 6 = <<24-6=18>>18 diaries.
#### 18