To find the number that must be multiplied by 0.75 to obtain 6, you can set up the equation:
\[ 0.75 \times x = 6 \]
To solve for \( x \), divide both sides of the equation by 0.75:
\[ x = \frac{6}{0.75} \]
Next, calculate \( \frac{6}{0.75} \):
\[ x = \frac{6}{0.75} = 6 \div 0.75 = 6 \times \frac{100}{75} = 6 \times \frac{4}{3} = 8 \]
Thus, the number that must be multiplied by 0.75 to obtain 6 is:
\[ \boxed{8} \]