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so an eligible character for Heroic Intervention (HI) is if an enemy is within 3" (some can get 6") or 5"vert but in the rules it just states I have to move towards that enemy. So lets say I have a character that lets me HI then can I move towards the enemy but not get in engagement range of them?

I don't see any requirement to end within engagement range, so your assessment appears correct.

You can move any direction, and any distance, as long as you end your move closer to the closest enemy model.