Your teacher has given you good advice.
Group pairs of terms with the same variable.
(x² +16x) +(y² -6y) = -24
Inside each parentheses, add the square of half the coefficient of the linear term. Of course, you add the same quantity on the right.
(x² +16x +8²) +(y² -6y +3²) = -24 +8² +3²
Write as squares.
(x +8)² +(y -3)² = 7²
Compare to the form of the equation of a circle with center at (h, k) and radius r.
(x -h)² +(y -k)² = r²
You see that (h, k) = (-8, 3) and r = 7.
The center of the circle is (-8, 3) and its radius is 7.