Answer
$L'=4L$
Work Step by Step
The period of a pendulum can be found using the formula $$T=2\pi \sqrt{\frac{l}{g}}$$ If the length of the pendulum is $4L$, the new period is $$T'=2\pi\sqrt{\frac{4l}{g}}=4\pi\sqrt{\frac{l}{g}}=2T$$ Therefore, if the length of the pendulum becomes 4L, the period will become 2T.