1. Write the given relation

   $z = \frac{a^2 b^{2/3}}{\sqrt{c}\, d^3}$

   We use the rule for maximum percentage error:

   • If $z = a^m b^n c^p \dots$, then $\frac{\Delta z}{z}\times 100 = |m|\frac{\Delta a}{a}\times 100 + |n|\frac{\Delta b}{b}\times 100 + |p|\frac{\Delta c}{c}\times 100 + \cdots$

2. Identify the powers of each variable

   Rewrite the expression as

   $z = a^2 b^{2/3} c^{-1/2} d^{-3}$

   So the exponents are:

   • for $a$: $2$
   • for $b$: $\frac{2}{3}$
   • for $c$: $-\frac{1}{2}$
   • for $d$: $-3$

3. Use the given percentage errors

   • Error in $a = 2\%$
   • Error in $b = 1.5\%$
   • Error in $c = 4\%$
   • Error in $d = 2.5\%$

   Therefore,

   $\%\text{ error in } z = 2(2) + \frac{2}{3}(1.5) + \frac{1}{2}(4) + 3(2.5)$

4. Calculate each term

   $2(2) = 4$ $\frac{2}{3}(1.5) = 1$ $\frac{1}{2}(4) = 2$ $3(2.5) = 7.5$

5. Add them

   $4 + 1 + 2 + 7.5 = 14.5$

6. Final answer

   $\boxed{14.5\%}$

So, the correct option is B.