How to write this equation in latex?
I wrote this code but not getting it.
E_{t-2}P_t=\frac{1}{2}(E_{t-2}m_t+\underbrace{E_{t-2}v_t}_\textrm{=0}-\underbrace{E_{t-2}u_t}_\textrm{=0}+(\frac{(1-\zeta )}{2})(\underbrace{E_{t-2}E_{t-1}P_t}_\textrm{=E_{t-2}}+\underbrace{E_{t-2}E_{t-2}P_t}_\textrm{=E_{t-2}})+(\frac{\zeta }{2})(E_{t-2}P_{t-1}+E_{t-2}P_{t-2})
You're almost there. Instead of
\underbrace{E_{t-2}v_t}_\textrm{=0}
type
\underbrace{E_{t-2}v_t}_{=0}
etc
I would also introduce some line breaks in the long equation.
\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator{\E}{E}
\begin{document}
\begin{multline*}
\E_{t-2}P_t=
\frac{1}{2}\Bigl(\E_{t-2}m_t
+\underbrace{\E_{t-2}v_t}_{=0}
-\underbrace{\E_{t-2}u_t}_{=0}\Bigr) \\
+\frac{(1-\zeta )}{2}\Bigl(
\underbrace{\E_{t-2}\E_{t-1}P_t}_{=\E_{t-2}}+
\underbrace{\E_{t-2}\E_{t-2}P_t}_{=\E_{t-2}}\Bigr) \\
+\frac{\zeta }{2}\Bigl(\E_{t-2}P_{t-1}+\E_{t-2}P_{t-2}\Bigr)
\end{multline*}
\end{document}
You can use Mathpix to generate LaTeX code for any mathematical equation by simply taking a screenshot of the equation. It will save you tons of time in future like it did for me after I discovered it!
$$ to start and stop an unnumbered displayed equation -- definitely not good practice for a LaTeX document.) It would be more impressive if you demonstrated that working with the OP's screenshot led to a satisfactory chunk of LaTeX code.
\usepackages to make your code compilable..texfile and try to compile it, it won't work. So then I have to do the job of adding a template, with a\documentclassand perhaps\usepackage{amsmath}and so on,\begin{document}etc. and you could have saved me that tiny chore. It's polite and helps us to help you.