First, solve for \( \left|y - 6\right| \):

\( \left|y - 6\right| \) - 9 = 8
\( \left|y - 6\right| \) = 8 + 9
\( \left|y - 6\right| \) = 17

The value inside the absolute value brackets can be either positive or negative so (y - 6) must equal + 17 or -17 for \( \left|y - 6\right| \) to equal 17:

So, y = -11 or y = 23.

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 45% the radius (and, consequently, the total area) increases by \( \frac{45\text{%}}{2} \) = 22\(\frac{1}{2}\)%

The amount of flour you need is (2 - \(\frac{5}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{16}{8} \) - \( \frac{5}{8} \)) cups
\( \frac{11}{8} \) cups
1\(\frac{3}{8}\) cups

To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{6} \) ÷ \( \frac{3}{6} \) = \( \frac{1}{6} \) x \( \frac{6}{3} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{6} \) x \( \frac{6}{3} \) = \( \frac{1 x 6}{6 x 3} \) = \( \frac{6}{18} \) = \(\frac{1}{3}\)

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{10 + 6 + 10 + 6}{4} \) = \( \frac{32}{4} \) = 8