$\frac{2}{3}+\frac{4}{5}$ is—

The correct option is $1\frac{7}{15}$.

To add the fractions $\frac{2}{3}$ and $\frac{4}{5}$, we need to follow a few simple steps:

Step 1: Find a common denominator.
The denominators of the two fractions are 3 and 5. Since 3 and 5 are prime numbers, their Least Common Multiple (LCM) is:
$3\times 5=15$

Step 2: Convert each fraction into an equivalent fraction with a denominator of 15.

For the first fraction, $\frac{2}{3}$, multiply both the numerator and denominator by 5:
$\frac{2}{3}=\frac{2\times 5}{3\times 5}$

For the second fraction, $\frac{4}{5}$, multiply both the numerator and denominator by 3:
$\frac{4}{5}=\frac{4\times 3}{5\times 3}$

Step 3: Add the numerators while keeping the common denominator.

$\frac{10}{15}+\frac{12}{15}=\frac{10+12}{15}=\frac{22}{15}$

Step 4: Convert the improper fraction to a mixed fraction.
Divide the numerator (22) by the denominator (15):
22 ÷ 15 = 1 with a remainder of 7.

Thus, $\frac{22}{15}$ can be written as the mixed number:

$1\frac{7}{15}$