In William Shakespeare's play "Romeo and Juliet," when Juliet tells Friar Laurence that "this shall slay them both," she is referring to the potion he has given her. The potion will induce a death-like sleep, allowing Juliet to escape her impending marriage to Paris and reunite with Romeo.
The "this" refers to the vial of potion that the Friar has provided to Juliet to help her avoid marrying Paris. The "both" refers to Juliet and Romeo. Juliet believes that by taking the potion, she will enable a series of events that could ultimately lead to the both of them dying if things go awry. The line exemplifies Juliet's desperation and determination, showing that she feels the need to take drastic measures to be with Romeo, even if those measures could lead to their deaths.
Evidence from the text supports this interpretation. In Act 4, Scene 1, Juliet expresses her despair and desperation over the situation with Paris and expresses her willingness to die rather than live without Romeo. She states:
"If, rather than to marry County Paris,
Thou hast the strength of will to slay thyself,
Then it is likely that thou will succeed in your plan."
This line demonstrates her desperation and foreshadows the tragic conclusion of the play, where their plan ultimately leads to their untimely deaths.