The data this claim seems to be based on is severely limited. I applaud their efforts to bring attention to this issue, but they do not appear to be using scientific counting methods, and their data only goes back a few years.
Although not explicitly stated in the claim, the claim appears to be specific to the United States.
This document published by the Human Rights Campaign (HRC) appears to be the source of the 2015 murder numbers in the image. It gives names, pictures and details of 21 trans people murdered in 2015. They do not give details on how they found or verified these names. On page 27 it discusses how the FBI's data collection methods undercount anti-trans violence. The FBI tables for 2015 list 1 trans person murdered.
The HRC report says of the FBI's numbers.
The FBI has taken important steps toward improving data collection for bias-motivated crimes based on gender identity and expression, but the most
recent data reported (2013) suggests that local jurisdictions fail to report many of these crimes, including homicides, as bias motivated.
Note: This report was published in 2015, when the FBI numbers I just linked were not available.
Based on the HRC's discussion of the challenges of collecting data, I believe their numbers are also an undercount. I applaud both their effort, and their openness about the weaknesses in their data.
The HRC states that "in 2009, the FBI began tracking bias-motivated crimes based on the victim’s actual or perceived gender identity." So not only are the FBI numbers an undercount, they don't go back very far in time.
This article, published by an advocacy group for LGBTQ issues, reports the number of murdered transgender people in 2016, but does not say where there data comes from. It also lists the names, and a few details for each murder. It repeats the claim, that 2016 was the deadliest year for trans people, but does not attempt to prove it by presenting any historical data.
In summary, I found what appears to be semi-quality data going back a few years that comes from independent organizations. The FBI, which should compile authoritative crime statistics, appears to be severely deficient on this count. The claim that 2016 had more anti-trans murders than any other year ever is not based on historical data.
If the claim were revised to say that 2016 had more trans murders than any year since 2013, that claim is grounded in some evidence. In recent years, trans people have gotten more organized, and gotten more media attention. It is entirely possible that the rate of trans murders is flat, but more of those murders are being recognized for what they truly are. The claim could be true, or it could be a case of reporting bias.