You have the following ${\color{#20A900} \mathbf{green}}$ and ${\color{#CEBB00} \mathbf{yellow}}$ $1 \times 1$ and $1 \times 2$ tiles:

How many ways can you use them to tile a $3 \times 2$ grid?

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Assumptions
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:

- The entire grid must be covered
- No overlaps or tiles outside the boundary
- The tiles can be oriented veritcally or horizontally
- You have exactly what is pictured, i.e. 1 green tile of each size and 1 yellow tile of each size

The answer is 44.

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Forget the colors for now...

For the 1x2 tiles they can be oriented:

Total: 11 ways

Now add in the colors:

For each of the above combinations, the colors on the squares can be exchanged (x2) and the colors on the rectangles can be exchanged (x2).

Total $= 11 \cdot 2 \cdot 2 = \boxed{44}$ ways