1. ~H
2. H v K
3. L >H
4. ~(K * ~L) v (~L * M) / M
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5. K 2,1 Disjunctive Syllogism
6. ~L 3,1 Modus Tollens
7. K * ~L 5,6 Conjunction
8. ~~(K * ~L) 7 Double Negation
9. ~L * M 4,8 Disjunctive Syllogism
10. M * ~L 9 Commutation
11. M 10 Simplification