Which of the following commands will print to standard out only the lines that do not begin with # (pound symbol) in the file foobar?

Without -v, this prints lines that DO begin with #, the opposite of what is required.

The -v flag tells grep to invert its output, printing only lines that do not match the pattern. The pattern ^# anchors to the beginning of the line, so together -v ^# outputs every line that does not start with a pound sign, which is exactly the desired behavior.

The pattern #$ matches lines that END with #, not lines that begin with it, and there is no inversion.

The pattern #$ matches lines ending with #, not lines beginning with it, so even with -v the result is inverted end-of-line matching, not start-of-line.