How is this 3/4 time?
 

If you look at the attachment in the third bar on the bass clef there is a quarter rest, two half notes and a quarter note, that adds up to 6 quarter note beats when only 3 are allowed. I've checked other transcriptions of the same piece and it's the same there too. What is going on? Plus, I don't understand that if a quarter rest is above a note does that mean that the rest is played before or after the note.

You are not suppose to add them up to get six just like you don't add the notes in the treble and bass clef to get six quarter notes in a single measure. It's simply B D B. The last bar in the bass clef can be written differently with rests and ties between quarter notes. But to make it easier it's written in two parts: on top a quarter rest then half note, on the bottom a half note then quarter note. The two parts are played at the same time. The B D B are played on the beat but you hold the B while you play the D then the play B again on the third beat.

Thanks for helping me out but I still don't get it. When you say that you're not supposed to add half notes together, on the contrary, in order to calculate if a bar accords with 3/4 time then it follows that one beat equals one-quarter note and there are to be three such beats in a bar. If two-quarter notes equals the same amount time as one-half note, then it follows that in the bass clef there are 6 beats, which is three too many. I still don't understand where the rest is supposed. Let's also break this down in terms of time. The tempo is set at 42 quarter notes per minute. 60/42 = 1.42. Hence two-quarter notes should be played 1.42 seconds apart and two half notes at 2.84 seconds apart. Each bar then should last 4.26 seconds. The bar in the bass clef would last 8.52 seconds.

The notes in the final measure of the bass clef overlap

It was an analogy. When you see bass and treble clef you're not adding all the notes together to get six quarter notes in the one measure. You understand there are two parts happening at the same time. Well the same is true in the bass clef in the third measure. There are two parts. The rest and the D note is one part, the B half-note and B quarter-note are another part. Each of part is in 3/4 time. Three notes: B D B. Each note is played are on the beat.

The composer wants the B to last for two beats, so he writes it as a half note, the D is to last two beats so he writes it as a half note. You're not to suppose to add there value together to get a whole note. All you have to do is play B D B on the beat. Three notes, three beats. There no other math involved.

I understand. Thank you for explaining this to me.

If you want to experiment with this, you can try to write scores yourself with a dedicated software. For instance using MuseScore, you will have to use the "voices" feature (buttons "1", "2", "3", "4" in the toolbar).

That's two voices in the bass clef. You can tell by the stems of the notes. The notes with down-stems are one voice and the note with the up-stem and quarter rest is another.

Well this is not a mistake. This is a separate style of performance. The uniqueness of a person, if I may say so.