First of all, I have a problem with the use of the word "anemia." Anemia by itself means that there is a reduced number of red blood cells and/or hemoglobin in the blood; however, there are hundreds of different types of anemia and a variety of causes depending on what type you have (Which you can read more about here). If you are "anemic" because of blood loss from falling and cutting yourself on a sharp object, for example, then you are going to need a transfusion and eating certain foods isn't going to help you. Hopefully that type of example would be obvious, but I try not underestimate what people what people will and won't do, particularly if medical care is not readily available to them for whatever reason. But for the sake of seeking out the original intent of this infographic, however, we will assume that this infographic speaks to anemia as a result of limited intake of iron.
Second of all, we also need to recognize the type of iron that your body absorbs the best from from food (aka the most bioavailable) is a type of iron called "heme iron" that is only found in animal protein sources (Link with links to other sources). So if someone is looking to get what is truly best absorbed, vegetable sources or non-heme iron simply does not fit the bill. The other related problems are that sometimes you are not going to eat enough of a certain food, like garlic, to be considered a good source of iron, and most plant tissue contains something called phytic acid which can prevent iron from being absorbed by the body (Phytic acid by itself is not bad, it's how plants store the mineral phosphorus and might actually play a role in keeping us from absorbing too much of certain minerals. Like anything else, it's the amount that matters). So as a primary way of preventing anemia, I wouldn't put any of these on my top eight list.
"That's nice SkepticRD, but I refuse to eat animal products for [insert reason here] or I have trouble buying sources of heme iron for [insert reason here] and what I really want to do is see if there is something I can do to help me absorb non-heme iron better."
Fair enough. First of all, go back to this link to find other, and sometimes better, sources of non-heme iron that are not listed here. Second of all, when it comes to beans, nuts, and grains you can try soaking (48 hours or more), sprouting, and cooking to activate the enzymes in the plants that break down phytic acid. Third, you can include more vegetables that have been fermented in your diet. Fourth, you can make sure that you eat the non-heme iron foods with vitamin C rich fruit and vegetables. Fifth, be aware of foods that you are eating that are rich in calcium as they can also prohibit absorption of iron rich foods. Sixth, you can realize that there is a lot of work involved in doing all of the above steps, and you might want to have some compassion on those who choose to get their iron from heme sources.
Take home message---If you have anemia, discuss this with your physician to try to determine what type of anemia and potential causes. If you need to improve your diet, go for the heme sources or be prepared to do a little more work for the non-heme ones.