Can a 20 years old boy get a hair transplant?

You need an examination by a doctor to make a diagnosis. Next step after that are treatment options.  Surgery may or may not be an option depending on your exam.  

Unfortunately, surgical hair restoration is generally not advised for patients younger than 25 with androgenetic alopecia (male pattern baldness) for two important reasons: 1) in a young person, we cannot tell if the donor area will be stable over time and 2) the earlier one’s hair loss begins, the more extensive it will likely become. Let’s explore each of these points:1. Predicting Donor Area StabilitySuccessful hair transplants require a stable donor zone. A donor zone is the area on the back and sides of the scalp where hair follicles are not affected by the hormone dihydrotestosterone (DHT). DHT is a byproduct of testosterone, the hormone that causes susceptible hair follicles on the scalp to shrink and eventually disappear. In a hair transplant, these hair follicles are replaced by DHT resistant hair follicles taken from the donor area.In a young person, particularly one younger than 25, it is very difficult, if not impossible, to accurately determine the stability of ones donor area, i.e. to tell for sure if the hair in the donor area will be resistant to DHT over the long-term. If a surgeon performs a hair transplant on a patient who has an unstable donor area, the transplanted hair will disappear over time.Not only does this cause the cosmetic benefit of the transplant to be lost, but the thinning donor area can reveal the donor scars that would normally be covered by hair – and this goes for both the linear scar of FUT and the small round scars of FUE.We often hear a young person who is desperate to have a hair transplant reason as follows: if my transplant fails, I’m no worse off than I was before I started, so I’ll take a chance that my donor area will be stable; On the other hand, if my donor area turns out not to be stable and the hair transplant fails, then I’ll just shave my head.This logic is flawed, however, since after a hair transplant shaving one’s head is no longer an option. This is because, as stated above, all hair transplants leave scars in the donor area. Whether the patient has a strip scar, in the case of FUT, or many tiny scars, in the case of FUE, the scars would be both noticeable and unsightly when the head is shaved.2. Early Hair Loss Usually Means Extensive BaldingGenerally, the younger one begins to lose hair, the more likely the hair loss will become extensive. And with extensive hair loss, there is usually not enough donor hair to cover the entire bald area. In someone with significant hair loss a hair transplant will usually only be able to replace hair on the front and top of the scalp, not on the sides (the temples) or on the back of the head (the crown). This look is fine for a person in their 30′s or 40′s who is losing hair, but for someone in their early 20s, having a thin or bald crown may make their appearance noticeably worse.In this case, medical therapy with finasteride (Propecia) is the most reasonable course of action. Finasteride has the ability to stop and potentially reverse the balding process for many years. This is why it is important for patients with early hair loss to start finasteride as soon as possible, to preserve as much of their hair as they can.

You are very wise to be trying to collect all the facts. Hair transplantation is usually not an option for men until the mid 20s. The more bald you are likely to become in life the more conservative your hair transplant surgeon needs to be with placement of the hairline and density to create. You should visit a few surgeons to understand what options are available right now for you including finasteride, minoxidil, LLLT (low level laser therapy) and platelet rich plasma. 

You should NOT have a hair transplant. Your biggest enemy is the
progressive thinning leading to a balding pattern that is not evident at this
point in time. The degree of thinning that might be showing would suggest that
you should see a doctor who most likely will get Bulk Measurements of your hair
to determine the degree of the thinning that you are presently having. If the
diagnosis is early genetic hair loss, then the best treatment would be the drug
finasteride which is highly effective in men of your age and may not only stop
the hair loss but possibly reverse it. If you are developing a more advanced
balding pattern the best test to get will determine the Bulk Measurements of
your hair and this will show, over a one-year time frame, how effective the
treatment will be. Once you know this information, then you and your doctor
need to develop a MASTER PLAN which will define what you need to do over the
years to come.

I imagine your expectations would be for a full head of hair to last your lifetime. It is unlikely that hair transplantation will accomplish this. You should go, along with your father, for a consultation with an experienced and reputable hair transplant surgeon.