The greatest size grid squares she can make is; 12 inch by 12 inch.
Since, it follows from the task content that the poster at the artist's disposal is 12 inch by 30 inch, it follows that the smaller dimension of the poster is; 12inch.
It is the limiting dimension and hence, the greatest size grid squares she can make is; 12in by 12 inch.
Read more on grid squares;
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