6 + [2/3 + 4/3] x 5/2 ÷ 3/4 = ?

Step 1: Simplify the expressions inside the brackets.
$[2 + 1] = 3$
$[3 + 3] = 6$
The expression is now
$\frac{5 + 3 \cdot 5 + 3}{6 + 6 \times 2 + 4}$

Step 2: Perform the multiplications (following order of operations).
Numerator: $3 \cdot 5 = 15$ → $5 + 15 + 3$
Denominator: $6 \times 2 = 12$ → $6 + 12 + 4$

Step 3: Add in the numerator.
$5 + 15 = 20$
$20 + 3 = 23$
Add in the denominator.
$6 + 12 = 18$
$18 + 4 = 22$
The expression simplifies to
$\frac{23}{22}$

Final answer:
\dfrac{23{22}}