Since the multiplicative inverse of a fraction p/q is the fraction that swaps its numerator and denominator, i.e. q/p, we have that the inverse of 2/3 is 3/2.
So, if we multiply both sides of the equation by 3/2, we have
[tex]\dfrac{3}{2}\cdot\dfrac{2}{3}a=16\cdot\dfrac{3}{2}[/tex]
3/2 and 2/3 are multiplicative inverse of each other, and by definition this means that they give 1 when multiplied:
[tex]\dfrac{3}{2}\cdot\dfrac{2}{3}a=1\cdot a=a=16\cdot\dfrac{3}{2}[/tex]
On the right hand side, we have
[tex]16\cdot\dfrac{3}{2}=8\cdot 3=24[/tex]
And so the solution is [tex]a=24[/tex]
