Which letter-cluster will complete the given series?
\text{DHMX, GJKU, _________ , MNGO}

Let us trace the change rule independently for each letter position across the clusters:
1. First letter pattern:

$$\text{D}(4)\to \text{G}(7)\to \mathbf{J}(10)\to \text{M}(13)(\text{Pattern: }+3)$$

2. Second letter pattern:

$$\text{H}(8)\to \text{J}(10)\to \mathbf{L}(12)\to \text{N}(14)(\text{Pattern: }+2)$$

3. Third letter pattern:

$$\text{M}(13)\to \text{K}(11)\to \mathbf{I}(9)\to \text{G}(7)(\text{Pattern: }-2)$$

4. Fourth letter pattern:

$$\text{X}(24)\to \text{U}(21)\to \mathbf{R}(18)\to \text{O}(15)(\text{Pattern: }-3)$$

Combining these individual letters gives the missing cluster: JLIR.