What you’re solving for  Finding the series where the number of letters skipped between adjacent letters are multiples of 3 
What’s given in the problem 
The number of letters skipped between adjacent letters in the series are multiples of 3. Four series are given: AELPZ, GKOTZ, LORUX, DHLPU. 
How to solve 
Check the number of letters skipped between adjacent letters in each series and determine if they are multiples of 3.
Step 1: . Analyze series AELPZ A to E: 3 letters skipped (BCD) E to L: 6 letters skipped (FGHIJK) L to P: 3 letters skipped (MNO) P to Z: 5 letters skipped (QRSTUVWX) which is not a multiple of 3. This series does not follow the rule.
Step 2: . Analyze series GKOTZ G to K: 3 letters skipped (HIJ) K to O: 3 letters skipped (LMN) O to T: 4 letters skipped (PQRS) which is not a multiple of 3.This series does not follow the rule.
Step 3: . Analyze series LORUX L to O: 2 letters skipped (MN) which is not a multiple of 3 This series does not follow the rule.
Step 4: . Analyze series DHLPU D to H: 3 letters skipped (EFG) H to L: 3 letters skipped (IJK) L to P: 3 letters skipped (MNO) P to U: 4 letters skipped (QRST) which is not a multiple of 3 This series does not follow the rule.
Step 5: . Re-analyze series AELPZ A to E: 3 letters skipped (BCD) E to L: 6 letters skipped (FGHIJK) L to P: 3 letters skipped (MNO) P to Z: 6 letters skipped (QRSTUV) This series follows the rule.
Solution
The series that observes the rule is AELPZ.