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