このボタンを ___ ___ _★_ ___ 動きます。

The correct sentence order is: 'このボタンを 押す(1) と(0) 機械が(2) 自動で(3) 動きます。' (If you press this button, the machine will move automatically). Grammatical breakdown: '[Verb Dictionary Form] + と' indicates a natural consequence or automatic action (when/if you do X, Y happens). The subject of the second clause is '機械が' (the machine [subject]) and it moves '自動で' (automatically). The third position (★) is filled by '機械が' (Choice '機械が').