Bromination of both Z-but-2ene and E-but-2-ene involve syn and anti addition. So, there would be 4 products as suggested in the question. But, I don't understand the terminology of 'trans-addition', mentioned in the question.

• Uh, I think that the correct term should be "anti" not "trans" – CoffeeIsLife Jun 6 '17 at 2:24
• Why do you think there will be syn addition? – Zhe Jun 6 '17 at 2:29
• A screenshot or picture of written text is problematic as it cannot be indexed by our site search or other search engines. Chemistry.se is about the content, and your question is unlikely to be helpful in the future for other people. Please take a couple of minutes to transcribe the text, so that it can be found easily in the future. – Martin - マーチン Jun 6 '17 at 7:01
• @Martin Well, I am kinda underskilled at mhChem and with my mobile phone jt's hard to draw chemical structures. So, I am sorry. But I will edit the question. – Partha Sarker Jun 6 '17 at 8:06

Just like @QuantumAMERICCINO has pointed out, it's probably anti addition.

Furthermore, you seem to wonder why a syn compound doesn't form. It all lies in the mechanism of bromination:

The double bond in cis-2-butene polarises the $\ce{Br-Br}$ bond in a nearby $\ce{Br2}$ molecule. A $\ce{Br+}$ ion attacks the double bond and forms a bromonium ion.

The bromonium ion makes the adjacent carbon atoms electrophilic. The bromide may attack the most electrophilic out of them. Here, however, they are equivalent.

You should now be able to understand how the mechanism works.

• So how are there 4 products? – Partha Sarker Jun 6 '17 at 4:57
• What 4 products @Mockingbird360 – Pritt says Reinstate Monica Jun 6 '17 at 5:03
• M,N,O,P as suggested in the question. – Partha Sarker Jun 6 '17 at 5:04
• @Mockingbird360 Oh that, they are just stereoisomers. I showed in my example, the bromine attacking the left carbon. If it attacked the right one instead, you would get the enantiomer of the above compound. For a trans-2-butene you would get a meso product. – Pritt says Reinstate Monica Jun 6 '17 at 5:11