To find out how much of the mountain Della climbs over the two days, we need to add the fractions of the mountain she climbs each day.
On the first day, she climbs \( \frac{1}{4} \) of the mountain.
On the second day, she climbs \( \frac{2}{6} \) of the mountain.
First, let's simplify \( \frac{2}{6} \):
\[ \frac{2}{6} = \frac{1}{3} \]
Now we need to add \( \frac{1}{4} \) and \( \frac{1}{3} \). To do this, we need a common denominator. The least common multiple of 4 and 3 is 12.
Now we convert both fractions to have a denominator of 12:
\[ \frac{1}{4} = \frac{3}{12} \quad (\text{because } 1 \times 3 = 3 \text{ and } 4 \times 3 = 12) \] \[ \frac{1}{3} = \frac{4}{12} \quad (\text{because } 1 \times 4 = 4 \text{ and } 3 \times 4 = 12) \]
Now we can add the two fractions:
\[ \frac{3}{12} + \frac{4}{12} = \frac{3 + 4}{12} = \frac{7}{12} \]
Therefore, the total amount of the mountain that Della climbs over the two days is \( \frac{7}{12} \).