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Typically in other implementations, one of the columns of matching items is non-interactive, with the second list containing potential options and distractors for the learner to choose between. This limits the amount that the learner has to do to answer the problem, simplifying the activity to focus on the content.
Matching via Drag-and-Drop
Drag and drop solutions for this activity are typically extremely clunky, as you can see in this particularly awful-looking example:
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Overall, however, due to accessibility and usability concerns inherent to drag and drop, I would recommend avoiding using drag-and-drop for this activity type if other alternatives are considered acceptable. The action of dragging and dropping offers no significant inherent benefit to the activity, while introducing numerous potential issues.
Matching via Dropdown
One alternative to dragging and dropping for this activity type is using dropdown menus, which is how Blackboard and Canvas chose to implement this activity type:
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