Add the fractions $\frac{3}{6}+\frac{2}{8}$ and write the result in simplest form.

A) $\frac{5}{14}$
B) $\frac{5}{6}$
C) $\frac{3}{4}$
D) $\frac{1}{8}$
E) $\frac{5}{48}$

To add these fractions, we need to find a common denominator. The least common multiple of 6 and 8 is 24, so we can rewrite the fractions with denominators of 24:

$$\frac{3}{6}+\frac{2}{8}=\frac{3\times 4}{6\times 4}+\frac{2\times 3}{8\times 3}=\frac{12}{24}+\frac{6}{24}$$

Now we can add the numerators:

$$\frac{12}{24}+\frac{6}{24}=\frac{18}{24}$$

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 6:

$$\frac{18}{24}=\frac{3}{4}$$

So the final answer is $\boxed{\textbf{(C)}\ \frac34}$.