Find the ratio between the fourth proportional of 12, 16, 6 and the third proportional of 4, 6.

8 : 9

Forth proportion to a, b , c = $\frac{b\;\times\;c}{1}$

Fourth proportion to 12, 16, 6 = \(\frac{16\; \times\; 6}{12}\)

                                            = 8

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

Third proportion to 4, 6 = \(\frac{6\; \times\; 6}{4}\)

                                   = 9

Ratio = 8 : 9