OK, seeing as I think you've been given an impossible task (for someone at 101 level), I'm attaching the sheet music (see PDF below):
You'll see it's in 3/4 time. (Listen to that video while reading, btw.)
(Sorry it seems to be in a mix of languages! The instrument names are Italian, and the title is given in Greek and French... go figure...

It was just the first score I found.)
The first notes you hear begin in the
middle of the first bar (played by "oboi" (oboes) and "fagotti" (bassoons). That's what I meant by the "downbeat" (beat 1) missing: nothing is playing on beat 1 of that bar, so to start with we have no idea where to count from. (If we were watching a performance of the piece, we'd see the conductor drop his baton down on that missing beat.)
What I meant by the "first accented chord" is the notes in 2nd bar played by what's labelled "Pistoni" and Trombe" (trombones) and the strings ("Violini" etc). The number of beats until the 2nd similar chord - in bar 4 - is six beats, two bars of 3/4.
Those chords make the best markers to count from, because they are on beat 1 of their bar.
The main beat value (the pulse you count) is represented by the quarter notes (crotchets), like the last 2 notes in each of the bars played by the oboes. There are 3 beats of this value in each bar - regardless of what notes are being played. (Ie, you count the beats, according to the regular pulse, not the notes, which are all different lengths.)
The tempo "allegro moderato" means "moderately fast", and in the video I posted that amounts to a bpm (beats per minute) of around 100 - so you should be counting at a speed of a little less than 2 beats per second.
If there are terms I'm using here that you don't understand, feel free to ask - but really anyone undertaking this task should be familiar with all these terms to start with. I don't understand why you've been given such a complicated piece (I'm guessing the other choices you had were equally advanced?).