Physics problem: I don't understand why the answer is 4V, thanks?

there is not a question listed. Presumably it is what does the meter read.

1) 10k (meter) in parallel with 10k is 5k. So you have a voltage divider, V = 6(5/15) = 2 volts

2) 10k (meter) in parallel with 100 is 10000•100/10100 = 99.01 Ω
Voltage divider, V = 6(99.01/199.01) = 2.99 volts

answer is NOT 4 volts, not even close.

ideal voltmeter, V = 3 volts.