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