Well, short answer is that the synoptic gospels (Mark especially) could be read as implying that Jesus’ ministry lasted for only more or less a single year, since it mentions only one Passover. Based on this, as well as what is seen as clues within the synoptics - for example, in Mark 2:23-28 grain is eaten raw, which suggests early summer; in 6:39 it is spring since the grass is green; Jesus then goes to Jerusalem for Passover in 11:1, presumably during the same spring as chapter 6 - there is an idea that Jesus’ ministry in the synoptics actually lasted only for more or less a year: between one early summer or late spring and the next spring.
John’s, on the other hand, mentions three Passovers (Jesus’ ministry begins and ends in one), which would imply more or less a two year period (three if you’re being generous). Besides Passover, John also mentions an unspecified “feast of the Judaeans” in 5:1, while chapter 7 is set during Sukkoth, aka the Feast of Booths (cf. verse 2) and 10:22ff is set during Hannukah, aka the Feast of the Dedication.
Late March-late April (Spring): First Passover (2:13)
??: Unnamed feast (5:1)
(One year has elapsed)
Late March-late April (Spring): Second Passover (6:4)
Late September-late October (Autumn): Booths (7:1ff.)
Late November-late December (Winter): Dedication (10:22ff.)
(Two years have elapsed)
Late March-late April (Spring): Third Passover (11:55ff.)
While one may argue that the ‘one year ministry’ version is more compatible with Josephus’ references to some other contemporaneous prophetic figures (most of whom had very short careers) as well as with Jesus’ itinerant lifestyle and His disciples’ lack of formal occupations, which some people think would not work as well in the long run, one has to remember that Matthew, Mark, and Luke often arrange their (episodic) material differently, and so, even these clues are not exactly helpful in determining how long Jesus was out in public.