Come si usa l'analisi dimensionale per capire quanti secondi sono in 4 anni?

All there is behind the solution is the constant stream of multiplying. This is what dimensional analysis is all about. A conversion from one unit to another requires some sort of multiplier to change one unit to another.

Here is a list of these multipliers.
#1"in"=2.54"cm"#
#1"lb"=0.453592"kg"#
#1 " second"=1/60 "minute"#

If you want to switch these, all you need to do is to divide the non-one value with itself and the 1 to find the other, vice versa solution.

#1"cm"=0.393701"in"#
#1"kg"=2.20462"lb"#
#1 " minute"=60 " seconds"#

From there, we are ready to move on.
1 minute = 60 seconds
1 ora = 60 minuti
#60" seconds" xx 60" minutes"=3600 " seconds"=1" hour"#

24 hours = 1 day
365.25 days = 1 year (to account for leap years, the likelihood of the extra day out of 4 years is added.)

#3600" seconds" xx 24" hours" = 86,400" seconds"#

...and finally:
#86,400" seconds" xx 365.25" days" xx 4=#
#126,230,400" seconds"#