Simplify the denominator

Calculate the sum of the fractions in the denominator: $2/3 + 3/5 = (10 + 9)/15 = 19/15$.

$\frac{2}{3} + \frac{3}{5} = \frac{10+9}{15} = \frac{19}{15}$

Evaluate the first part

The expression is $1 / (19/15)$, which simplifies to the reciprocal: $15/19$.

$\frac{1}{\frac{19}{15}} = \frac{15}{19}$

Perform the final division

Now divide the result by $8/39$, which is equivalent to multiplying by $39/8$: $(15/19) \times (39/8) = (15 \times 39) / (19 \times 8)$.

$\frac{15}{19} \div \frac{8}{39} = \frac{15}{19} \times \frac{39}{8} = \frac{15 \times 39}{19 \times 8} = \frac{585}{152}$

Convert to mixed fraction

Divide 585 by 152 to get the mixed fraction form: $585 \div 152 = 3$ with a remainder of $585 - (3 \times 152) = 585 - 456 = 129$. So the result is $3 \frac{129}{152}$. Wait, checking the provided option C calculation: $15/19 * 39/8 = (15*39)/(19*8) = 585/152$. Let's re-verify: $39/19$ is approx 2.05. Re-check prompt: $15/19 * 39/8 = 585/152 = 3.848$. $3 + 28/33 \approx 3.848$. Correction: $15/19 * 39/8$ simplifying: $39/19$ is not integer. Let's re-check $15 * 39 / (19 * 8) = 585 / 152$. $3 * 152 = 456$. $585 - 456 = 129$. The answer is $3 \frac{129}{152}$. Re-checking the provided options: Option C is $3 \frac{28}{33}$. Perhaps there is a typo in my reading or the question? Recalculating: $2/3 + 3/5 = 19/15$. $1 / (19/15) = 15/19$. $15/19 / (8/39) = 15/19 * 39/8 = 585/152$. If the input meant $(1 / (2/3) + 3/5) / (8/39)$, it would be different. Given the official key is C, let's assume the question meant $(3/2 + 3/5) / (8/39) = (21/10) * (39/8) = 819/80 \approx 10.23$. No. What if it is $1 / (2/3 + 3/5) = 15/19$. Maybe it is $15/19 / (8/39) = 585/152$. Let's trust the algebraic steps.

$3 \frac{129}{152}$