Let's denote the unknown number as \( x \). According to the problem, one-quarter of the difference between the number and 3 is equal to 2. We can express this mathematically as:
\[ \frac{1}{4}(x - 3) = 2 \]
To eliminate the fraction, multiply both sides of the equation by 4:
\[ x - 3 = 8 \]
Now, solve for \( x \) by adding 3 to both sides:
\[ x = 8 + 3 \]
\[ x = 11 \]
Therefore, the number is 11.
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