To find out how many square yards the goats will be allowed to roam in, we first need to calculate the area of the larger fenced area for the goats and then subtract the area of the garden.
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Area of the area for the goats: \[ \text{Area of goats' fence} = \text{length} \times \text{width} = 12 , \text{yd} \times 15 , \text{yd} = 180 , \text{yd}^2 \]
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Area of the garden: \[ \text{Area of garden} = \text{length} \times \text{width} = 3 , \text{yd} \times 6 , \text{yd} = 18 , \text{yd}^2 \]
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Area available for the goats: \[ \text{Area for goats} = \text{Area of goats' fence} - \text{Area of garden} = 180 , \text{yd}^2 - 18 , \text{yd}^2 = 162 , \text{yd}^2 \]
Thus, the fenced area that the goats will be allowed to roam in is 162 yd².