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