There are two puzzles with shapes and numbers. The first has Star = 80, Triangle = 10, Right = 12, and Left = ?. The second has Star = 60, Left = 120, Triangle = 4, and Right = ?. Find the missing num

In the second puzzle, we have the numbers: Star = 60, Left = 120, Triangle = 4, Right = ?
Let the unknown right number be $Y$.
We observe the pattern: (Left number) $\times$ (Triangle number) $\div$ (Right number) = (Star number).
Substitute the known values:

$$120 \times 4 \div Y = 60$$ $$480 \div Y = 60$$

To solve for $Y$, we rearrange the equation:

$$Y = \frac{480}{60}$$ $$Y = 8$$

We can verify this pattern: $120 \times 4 \div 8 = 480 \div 8 = 60$. This matches the star number.

In the first puzzle, we have the numbers: Star = 80, Triangle = 10, Right = 12, Left = ?
Let the unknown left number be $X$.
Using the pattern: (Left number) $\times$ (Triangle number) $\div$ (Right number) = (Star number).

$$X \times 10 \div 12 = 80$$

To solve for $X$:

$$\frac{10X}{12} = 80$$

Simplify the fraction $\frac{10}{12}$ to $\frac{5}{6}$:

$$\frac{5X}{6} = 80$$

Multiply both sides by 6:

$$5X = 80 \times 6$$ $$5X = 480$$

Divide both sides by 5:

$$X = \frac{480}{5}$$ $$X = 96$$

The missing number in the blue box for the first puzzle is $\boxed{\text{96}}$.

In the second puzzle, we have the numbers: Star = 60, Left = 120, Triangle = 4, Right = ?
Let the unknown right number be $Y$.
Using the pattern: (Left number) $\times$ (Triangle number) $\div$ (Right number) = (Star number).

$$120 \times 4 \div Y = 60$$

To solve for $Y$:

$$480 \div Y = 60$$ $$Y = \frac{480}{60}$$ $$Y = 8$$

The missing number in the blue box for the second puzzle is $\boxed{\text{8}}$.