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Someone else might know better than me but I think it’s the high pressure fuel line to the injectors, although it might be a vacuum line.
The damage looks like it has been caused by a mouse or rat chewing the hose, either way it needs replacing and a way of discouraging the rodent in case of future attacks.
2020 blue SZ5 (one of the last to be registered in the UK)
Ex 2011 Blue Jimny SZ4
Northumberland Jimny Blog
That would be "hose, fuel return" - the round object it's attached to on the left end is the fuel pressure regulator, and that is bolted to the fuel rail that feeds the injectors.
Here's how the system works, the fuel pump supplies fuel under pressure to the rail and through it to the injectors, the regulator is at the end of the rail and allows "excess fuel" to return to the tank through that hose.
It can be replaced with hose of the correct diameter as long as it is rated for petrol, it's not a high pressure hose.
Suzuki supplies it as "bulk hose" that you then cut to the correct length,
