Suppose $\cos V = \frac{2}{3}$ in the diagram below.  What is $TV$?



[asy]
pair T,U,V;
V = (0,0);
T = (0,16);
U = (17.89,16);
draw(V--T--U--V);
draw(rightanglemark(V,T,U,23));
label("$V$",V,SW);
label("$U$",U,NE);
label("$T$",T,NW);
label("$24$",(U-V)/2,SE);
[/asy]
Since $\cos V = \frac{2}{3}$ and $\cos V = \frac{TV}{UV}=\frac{TV}{24}$, we have $\frac{TV}{24} = \frac{2}{3}$, so $TV = \frac{2}{3} \cdot 24 = \boxed{16}$.