If the first two terms in H.P are 24 and 12, then the 4^th term is

Since the reciprocals are in AP, $\frac{1}{24},\frac{1}{12},\frac{1}{x}$  are in A.P

i.e., $\frac{1}{x}-\frac{1}{12}=\frac{1}{12}-\frac{1}{24}$

$\frac{1}{x}=\frac{1}{6}-\frac{1}{24}=\frac{1}{8}$

Let the 4^th term $=y$

$\frac{1}{y}-\frac{1}{8}=\frac{1}{8}-\frac{1}{12}$

$\frac{1}{y}=\frac{1}{6}$

$y=6$

Required answer, 4^th term $=6$