1. From what I can make out of the scan, this questio is about COMPTON SCATTERING.
Compton scattering is the collision between an electromagnetic wave in the form of an x-ray, and an electron
“Normally” it may be “expected” that an x-ray would interact with an electron – or any other charged body – by making it OSCILLATE, and thus radiate energy connected to the frequency and mode of its oscillations.
The electron may or may not be expected to actually physically move from where it was before the wave came at it. If it oscillates it moves, yes, but around its centre of oscillation.
What Compton did (Nobel prize for doing it, it seems) was to demonstrate that an electromagnetic wave in the x-ray part of the spectrum could be made to “bounce” off an electron, as though BOTH were particles, the electron being a charged particle, the x-ray photon being uncharged.
And this showed that the x-ray WAVE could also BEHAVE as though it were a PARTICLE.
It is also the case, I believe, that an ELECTRON PARTICLE can BEHAVE as though it were a WAVE. An idea which is used in ELECTRON MICROSCOPY.

3. The energy of the ELASTICALLY scattered x-ray ...
BEFORE COLLISION
AFTER COLLISION
X-RAY photon
ELECTRON
X-RAY PHOTON
IF this is correct, then I’m baffled by the weird way it is “demanded” that it’s answered.
There also seems to be far too much information in the introductory box for this question, which makes me wonder if there are other questions on the same theme.