Name the table on the left "Data" and the table on the right "Summary".
In the table table summary add a header row and a footer row. In my example the header is row 1 and the footer is row 13:
For the table on the right (title "Summary") make the header row contain the titles as show. Also enter the categories as show. in column A of the footer enter the text "Total"
this is shorthand for select cell B2 and type (or copy and paste from here) the formula:
now select B2, and fill down by hovering the cirsor over the bottom edge and drag the yellow circle down as needed.
In the footer row (in this example B13) enter the formula:
Please let us know if you have other questions
It's a good start. Make the bottom row of each Table a Footer Row so we can put summary calculations there without it getting confused with the input data.
Also, name your tables so we can refer to them in equations. Select both tables and then in the Table Inspector, click on Table Name. I suggest calling the one on the left Entries and the one on the right Summary.
Then, in B2 of Summary, we'll enter the following equation:
=SUMIF(Entries::A, A, Entries::B)
Fill Down by dragging the fill handle in the middle of the bottom cell border. Stop just above the Footer Row where the total will be. In the Column B Footer cell, write: =SUM(B).
That shoud do it. There were lots of steps there, so ask about any you don't understand.