Fourth proportion to 12, 18, 6 is equal to the third proportion to 4, k. What is the value of k?

6

Fourth proportion to a, b, c = $\frac{b\; \times\;c}{a}$

Fourth proportion to 12, 18, 6 = $\frac{18\; \times\; 6}{12}$

                                            = 9

Third proportion to a, b = $\frac{b\; \times\; b}{a}$

Third proportion to 4, k = $\frac{k\; \times\; k}{4}$

         We know, this is equal to 9 

$\frac{k^2}{4}$ = 9 

k² = 36 or k = 6