Hi this is a repost, and I have another 2 questions I posted yesterday. Please help me with these, I need help to verify my work, not confident if I'm doing these right.

Use oxidation numbers to identify if this reaction is REDOX reactions.

3NO2(g) + H2O(l) �� 2HNO3(aq) + NO(g)

3NO2 = -3 for N
= -2 for o2

H2O = +1 for H2
= -2 for O

---->

2HNO3 = +1 for 2H
= -3 for N
= -2 for O3

NO = -3 for N
= -2 for O

Therefore Nitrogen is reduced (one -3 remains on right side)
hence REDOX has occured

Is this right? Also should I be multiplying oxidation numbers if there is a number in front ie. 2SO = -2 oxidation but should I multiply by the 2 infront so is now -4 oxidation for sulphur in 2SO? Please let me know because I haven't done this and if wrong need to correct for a lot of questions :(

What you have done confuses me; in a class I could ask a question or two and know how to answer.

The first equation is redox so you are correct; however, not for the reason you cite(-3 N left over on one side versus the other).
The oxidation state for N in NO2 is +4 and not -3. How do you get that? Each O is -2 and there are two of them for a total of -4; therefore, for NO2 to be zero N must be +4. On the right side, each N is +5 in HNO3 and +2 in NO. This is a redox equation because you have something being oxidized and something being reduced (in this case it just happens to be N in NO2---it goes both ways).
As to multiplying by the coefficient, it depends. To identify if redox has occurred, you want to see that EACH atom has changed and I don't multiply by the coefficient to determine that since it isn't needed. In fact, it can be confusing in some situations (such as this one).

So when do I multiply by the coefficient? When I am balancing equations, we want to know the TOTAL charge on side going to a TOTAL charge on the other. In the example you cite for 2SO, here are the two ways of doing it.
#1. Each O is -2, for SO to be zero then S must be +2.

#2. Each O is -2 and that x 2 = -4 for both O atoms. Therefore, both S atoms must be +4 or EACH must be +2. Doing it this way just increases the number or steps (the work) AND the chance of making a mistake.

Yes, your explanation is mostly correct. To verify if a reaction is a redox reaction, you need to check if there is a change in the oxidation numbers of any of the elements involved in the reaction.

In the given reaction:

3NO2(g) + H2O(l) ⟶ 2HNO3(aq) + NO(g)

You correctly determined the oxidation numbers as:

3NO2: -3 for N, -2 for O
H2O: +1 for H, -2 for O
2HNO3: +1 for H, -3 for N, -2 for O
NO: -3 for N, -2 for O

You observed that nitrogen (N) undergoes a change in oxidation state from -3 in NO2 to -3 in NO (remaining the same). This indicates that the reaction involves oxidation and reduction, making it a redox reaction.

Regarding your second question, if there is a number in front of a compound (like 2SO), you do not multiply the oxidation number for each element. The oxidation number applies to each individual element within the compound. So for 2SO, the oxidation number for sulfur (S) would still be -2.

Remember to consider the oxidation numbers of individual atoms within a compound and how they change during the reaction to identify if a reaction is redox or not.