This is a much harder problem that it appears at first glance.
The sort solution proposed by danmero should just give one line sort each set of lines with identical values in the 1st 2 fields, but the one printed depends on the sort order of the remaining fields. The order ginkrf requested was that the last line in the (unsorted) file be printed for each set of lines with identical values in the 1st two fields.

The awk solution proposed by mjf will print the 1st line of each matching set instead of the last line of each matching set. (And, if the 1st 2 fields when concatenated yield the same key even though the fields are different, some desired output lines may be skipped. For example if $1 is "ab" and $2 is "c" in one record and "a" and "bc" in another, they will both have key "abc".)

Since ginkrf didn't say whether the order of the lines in the output has to match the order in which they appeared in the input, I won't try to guess at an efficient way to do what has been requested. If the order is important, the input file could be reversed, fed through mfj's awk script (with !x[$1 $2]++ changed to !x[$1,$2]++), and then reverse the order of the output again. Depending on the output constraints this might or might not be grossly inefficient.

If the output order is not important, it could be done easily with an awk script, but could require almost 400mb of virtual address space to process 20 million 20 byte records.

With a better description of the input (is there anything in a record other than its position in the input that can be used to determine which of several lines with the 1st two fields matching should be printed) and the output constraints, we might be able to provide a better solution. Are there ever more than two lines with the same 1st two fields? If yes, out of the 20 million input records, how many output records do you expect to be produced? Are there likely to be lots of lines that only have one occurrence of the 1st two fields? What are the file sizes (input and output) in bytes (instead of records)? What is the longest input line in bytes?

What OS and hardware are you using? How much memory? How much swap space?