What is the independent variable in this memory experiment?
It seems this experiment is trying to test two different things:

If participants falsely recognize (respond &quot;yes&quot;) to more similar
sounding unstudied words than unrelated unstudied words it is taken as
evidence that they encoded the sound of the words they studied.

For this part of the experiment, the independent variable is the type of word on the recognition test, specifically whether the words on the recognition test sound similar to the studied words or not. In this case, the dependent variable is the likelihood of recognizing the words, with the hypothesis being that participants will be more likely to recognize words that sound similar to the studied words than words that are unrelated to the studied words.

Comparing &quot;yes&quot; responses between unstudied words that sound similar
to remember instructed study words and those that sound similar to
forget instructed study words can reveal whether the process of
remembering or forgetting is more likely to lead to the encoding of
sound.

For this part of the experiment, the independent variable is the memory-instruction (and whether words on the test sound like remember-instructed or forget-instructed words, since these variables go hand-in-hand). In this case, the dependent variable is still the likelihood of recognizing the words, with the hypothesis (probably) being that participants will be more likely to recognize words that sound similar to remember-instructed words than words that sound similar to forget-instructed words.
Edit: I just realized you designed the experiment. I would recommend choosing a single hypothesis because there seem to be two hypotheses and corresponding independent variables which makes things kind of confusing.