While planning the Beechwood School Carnival, the principal predicted how many people would attend. On the day of the carnival, 150 people came. The principal's prediction was 20% less than that. How many people did the principal predict would attend?

Let the number of people predicted by the principal be denoted as \( P \).

According to the problem, the prediction was 20% less than the actual attendance of 150 people. This means we can express \( P \) as:

\[ P = 150 - 0.20 \times 150 \]

Calculating \( 0.20 \times 150 \):

\[ 0.20 \times 150 = 30 \]

Now substituting this back into the equation for \( P \):

\[ P = 150 - 30 \] \[ P = 120 \]

Thus, the principal predicted that \( \boxed{120} \) people would attend the carnival.