For these type of questions, it requires you to understand and write a algebraic equation out of words given.
Therefore, let that number be y.
"if 9 is added to twice a number" = 2y + 9
"this sum is multiplied by six" = (2y + 9) x 6
"the number is multiplied by 7" = 7y
"14 is added to the product" = 7y + 14
Now combine the expressions and solve away!
(2y + 9) x 6 = 7y + 14
Expand.
12y + 54 = 7y + 14
Shift all the y to a side and all the pure numbers to another side.
12y - 7y = 14 - 54
Group them.
5y = - 40
Divide 5 on both sides.
y = - 8
Therefore, the number is - 8.