Solution

For naming the given compound ; $$H_{3}C-CH_{2}-CO-CH_{2}-CO-COOH$$, the following steps are followed:
i) The parent chain consists of six carbon atoms and the primary functional group is -COOH , thus the suffix -oic acid.
ii) The two secondary functional groups are -CO, thus the prefix -oxo is used for them.
iii) Numbering the compound is done from right to left, as lowest number is given to the -COOH group and also in accordance with the least sum rule for secondary functional groups.
Thus the name of the compound is 2,4-dioxohexanoic acid