4 consecutive odd integers such as that the opposite of the third to twice the first equals the product of three and the second

Answer 1

let the 4 numbers be
x, x+2, x+4, x+6
(-x - 4)(2)(x) = 3(x+2)
-2x^2 - 8x = 3x + 6
2x^2 + 11x + 6 = 0

This does not have an integer solution, so either your question is bogus
or my interpretation of "the opposite of the third to twice the first" is wrong