what is a combined technique that transfers DNA from gel electrophoresis to a membrane, then detects specific DNA sequences?

The correct answer would be southern blotting.

Southern blotting is technique used in molecular biology to determine the presence of specific DNA sequence in DNA samples. It is named after the scientist Edwin Southern who first published it in 1975.

The steps involved in this technique are:

DNA digestion Gel electrophoresis Blotting or transfer of DNA from a gel to a membrane (usually nitro-cellulose membrane) Probing or addition of radioactive, fluorescent or enzyme labelled probes Hybridization and washing Detection.