Let's find the mode and median of the given frequency distribution step by step:

Given frequency distribution:

\[

\begin{array}{c|c}

\text{No. of children} & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\

\hline

\text{No. of families} & 7 & 11 & 6 & 7 & 7 & 5 & 3

\end{array}

\]

Step 1: Mode

The mode is the value that appears most frequently in the distribution. Looking at the given data, we can see that the value 1 appears the most frequently (11 times), making it the mode.

So, the mode is 1.

Step 2: Median

The median is the middle value of a data set when it is arranged in ascending order. First, let's arrange the data in ascending order along with their frequencies:

\[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6 \]

There are a total of \(7 + 11 + 6 + 7 + 7 + 5 + 3 = 46\) families.

The median is the middle value. Since there are 46 families, the median would be the average of the 23rd and 24th values in the ordered list:

\[ \text{Median} = \frac{2 + 2}{2} = 2 \]

So, the median is 2.