How can I escape a double quote inside double quotes?

Use a backslash:

echo "\""     # Prints one " character.

A simple example of escaping quotes in the shell:

$ echo 'abc'\''abc'
abc'abc
$ echo "abc"\""abc"
abc"abc

It's done by finishing an already-opened one ('), placing the escaped one (\'), and then opening another one (').

Alternatively:

$ echo 'abc'"'"'abc'
abc'abc
$ echo "abc"'"'"abc"
abc"abc

It's done by finishing already opened one ('), placing a quote in another quote ("'"), and then opening another one (').

More examples: Escaping single-quotes within single-quoted strings

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