Pilot reported having a near miss during landing with other aircraft landing on opposite end of runway due to miscommunication with ATC.

Narrative

At first glance; I was in LDA-C approach of VNY.Before enter IAF; I've got instruction from ATC to join right downwind for RWY 16R; but I didn't receive well. So; I read back as 'RWY 16L; join right downwind after SILIK(FAF)'. But controller didn't correct my read back; so I expected to use RWY 16L. And it was my first downwind inbound for VNY.Just after that; I felt something weird; and suspected about using right downwind for left RWY. Then checked the LDA-C for VNY chart again; but there is no restricted or prohibited with using LDA-C with using 16L on Day time.Then; after I get into the right downwind; I got a clearance to land 16R with advisory for caution of wake turbulence from private jet. But I misunderstood due to not familiar airport; and busy ATC communication; I read back as 'After private jets passed; cleared to land RWY 16L'.That moment; I believed RWY 16L is correct. And maybe controller suspected about my read back for landing clearance (maybe 'After private jets passed' was the problem); controller said 'Cleared to land; RWY 16R.'. Even that moment my thought was my assigned RWY is 16L; but I just missed to read back RWY Number. As ATC told anything; I tried to land 16L.Just exited from downwind and entered the right base; I just made head-on with another plane ATC said that plane has no factor to me. But I felt something dangerous; I took evasive action.Plane from opposite was made go-around.Finally; after events are end; ATC emphasized they told me to use RWY 16R; and clarified between me and ATC's miscommunication; so gave me other clearance to land 16L; and landed with last clearance.