When the data are IN ORDER, say lowest to highest, then the median is the "middle" data item where there are an equal number of data items ABOVE and BELOW.
Notice that your frequency table puts the items in order from low to high, and tells you that there are 100 items. So, the median should divide the whole group into two sets of 50...50 items ABOVE the median value and 50 items below the median value. So the median should be halfway between the 50th data item and the 51st data item. But look! Both the 50th data item and the 51st data item must be 14 (can you see that from the table? Items 50 and 51 are BOTH in that group of 15 items with a value of 14. SO.....median is 14.
Now...repeat this kind of process to find the median of the items BELOW 14, and the median of the items ABOVE 14. Those will be Q1 and Q3.
The table also shows you the minimum and the maximum data items....those, together with the location of Q1, Q2(median), and Q3 give you everything you need to create the box-and-whisker plot.