To find the correlation coefficient \( r \) for the linear equation \( Y = -\frac{3}{2}x + 6 \), note that the equation is in the slope-intercept form \( Y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
The correlation coefficient \( r \) indicates the strength and direction of the linear relationship between two variables. In the case of a simple linear regression, it can be derived from the slope \( m \).
Here, the slope \( m = -\frac{3}{2} \).
The correlation coefficient \( r \) is equal to the sign of the slope:
- If \( m > 0 \), \( r \) is positive.
- If \( m < 0 \), \( r \) is negative.
Since \( m = -\frac{3}{2} < 0 \), we conclude that \( r \) must be negative.
To find the exact value of \( r \), since we are dealing with a simple linear regression, \( r \) will be equal to the sign of the slope in this case as for perfect linear relationships:
\[ r = -1 \]
Thus, the correlation coefficient \( r \) is:
\[ \boxed{-1} \]