Fourth proportion to 12, 18, and 6 is same as the third proportion to k and 6. What is the value of k ?

4

Fourth proportion of A, B, C = $\frac{B\; \times\;C}{A}$

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

                                               = 9

Third proportional of A and B = \(\frac{B\; \times\;B}{A}\)

Third proportion to k, 6 = \(\frac{6\; \times\; 6}{k}\)

                            ⇒      9 = 36/k

                            ⇒      k = 4