Find closest multiple of $15$ to $144$. We see that $9 \times 15 = 135$ is the nearest. Now subtract $135$ from $144$ to get reminder $9$. Add $9$ to quotient.
Find closest multiple of $15$ to $90$. We see that $6 \times 15 = 90$ is the nearest. Now subtract $90$ from $90$ to get reminder $0$. Add $6$ to quotient.
Since $0$ is less than $15$, stop the division. The reminder is $0$. The topmost line $0096$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $96$.