What is the simplified form of 30 times x to the sixth power over 14 times y to the fifth power times the fraction 7 times y-squared over 6 times x to the fourth power ?

If we convert the given in its mathematical form, we have,

                      (30x⁶/14y⁵)(7y²/6x⁴)
It can be observed that the numerator of the first and the denominator of the second have a common factor of 6x⁴. Also, the denominator of the first and the numerator of the second expression have a common factor of 7y².

                      ((6x⁴)(5x²)/(7y²)(2y³))(7y²/6x⁴)

Cancellation of the common terms will give us an answer of,
  
                               5x²/2y³

Therefore, the simplified version of the involved operation is 5x²/2y³.