To determine the missing number that makes the two fractions equal, you can cross-multiply.
Starting with the equation:
\[ \frac{6}{10} = \frac{3}{x} \]
Cross-multiplying gives:
\[ 6 \cdot x = 3 \cdot 10 \]
This simplifies to:
\[ 6x = 30 \]
Now, divide both sides by 6 to solve for \(x\):
\[ x = \frac{30}{6} = 5 \]
So, the missing number is:
\[ \boxed{5} \]