For a closed organ pipe, the resonate frequency(harmonics) is an odd multiple of the fundamental frequency.

Therefore, $\left(2n-1\right)f_0\le 20000 \mathrm{Hz}$, where $n=1,2,3...$

$f_0=1.5 \mathrm{kHz}\Rightarrow$ fundamental frequency

Then, $n=7$

The total number of overtones that can be heard is $6$. ($2^{\mathrm{nd}}$ harmonic to $7^{\mathrm{th}}$ harmonic. )