  We study the exotic decay of the 125 GeV Higgs boson ($h$) into a pair of
light spin-0 particles ($\phi$) which subsequently decays and results in a $4b$
final state. This decay mode is well motivated in the Next to Minimal
Supersymmetric Standard Model (NMSSM) and extended Higgs sector models. Instead
of searching at the Large Hadron Collider (LHC) and the High Luminosity Large
Hadron Collider (HL-LHC) which are beset by large Standard Model (SM)
backgrounds, we investigate this decay channel at the much cleaner Large Hadron
Electron Collider (LHeC). With some simple selection cuts this channel becomes
nearly free of background at this $ep$ machine, in stark contrast with the
situation at the (HL-)LHC. With a parton level analysis we show that for the
$\phi$ mass range $[20,60]GeV$, with $100\,fb^{-1}$ luminosity the LHeC is
generally capable of constraining
$C_{4b}^2\equiv\kappa_{V}^2\times\text{Br}(h\rightarrow\phi\phi)\times\text{Br}^2(\phi\rightarrow
b\bar{b})$ ($\kappa_{V}$ denotes the $hVV(V=W,Z)$ coupling strength relative to
the SM value) to a few percent level ($95\%$ CLs). With $1\,ab^{-1}$ luminosity
$C_{4b}^2$ at a few per mille level can be probed. These sensitivities are much
better than the HL-LHC performance and demonstrate the important role expected
to be played by the LHeC in probing exotic Higgs decay processes, in addition
to the already proposed invisible Higgs decay channel.
