To find the volume of the solid Amy carved out of wood, we need to interpret the given dimensions. The dimensions seem to represent a composite solid, such as a block or a series of rectangular prisms.
Let's assume we are dealing with a rectangular prism and the dimensions given are the lengths of the edges. However, since we have 6 values, we might need to arrange them into dimensions of two or more prisms.
Let's consider if the solid can be divided or analyzed as rectangular prisms with the given dimensions:
-
Rectangular prism 1: with dimensions 6 in, 2 in, and 4 in. \[ V_1 = \text{length} \times \text{width} \times \text{height} = 6 , \text{in} \times 2 , \text{in} \times 4 , \text{in} = 48 , \text{in}^3 \]
-
Rectangular prism 2: with dimensions 2 in, 8 in, and 7 in. \[ V_2 = 2 , \text{in} \times 8 , \text{in} \times 7 , \text{in} = 112 , \text{in}^3 \]
Now we can find the total volume of the solid by adding the volumes of the two prisms: \[ V_{\text{total}} = V_1 + V_2 = 48 , \text{in}^3 + 112 , \text{in}^3 = 160 , \text{in}^3 \]
Thus, the volume of the solid is \( \boxed{160} , \text{in}^3 \).