The figure shows two 4-tile patterns. Either one or both of the patterns can be used any number of times and in any orientation to construct a new pattern. Which one of the options below **cannot** be constructed by using only these two 4-tile patterns assuming there are no overlaps among them?

Both given base patterns consist of exactly $4$ square units:

1. A $2 \times 2$ square tile pattern ($4$ squares)

2. A $4 \times 1$ (or $1 \times 4$) straight tile pattern ($4$ squares)

Any shape constructed from these patterns without overlapping must have a total area (number of squares) that is a multiple of $4$.

Let us calculate the total number of squares in each option:

• (A) Dimensions: $2 \times 4 = 8$ squares. Since $8$ is divisible by $4$, it can be constructed (e.g., by placing two $2 \times 2$ tiles side-by-side).

• (B) Dimensions: $3 \times 4 = 12$ squares. Since $12$ is divisible by $4$, it can be constructed (e.g., by stacking three $1 \times 4$ tiles horizontally).

• (C) Dimensions: $3 \times 6 = 18$ squares. Since $18$ is not divisible by $4$ ($18 \pmod 4 = 2$), it is impossible to construct this pattern using only $4$-tile units without overlap.

• (D) Dimensions: $4 \times 6 = 24$ squares. Since $24$ is divisible by $4$, it can be constructed (e.g., using six $2 \times 2$ tiles).

Hence, the pattern in (C) cannot be constructed.