Coins in Boxes

Assume that box 1 and 4 lie. Then boxes 2 and 3 have correct labels. Then silver is in 3 and gold is in 4. But box 1 has a false label and therefore box 2 has either all silver or all gold. We have a contradiction. Then either box 1 or 4 (or both) have a correct label.

Suppose now 2 and 4 lie. Then 3 told the truth (and 1). Then 4 has gold. But silver is not in 3 because 2 lied, and silver is not in 1 because 4 lied. Also, silver is not in 2 because 2 would have mixed. Then silver is in 4. This is a contradiction.

We then have that 2 or 4 tells the truth. Notice that 2 and 4 cannot be true at the same time. Since so far our options for true labels are 1, 2, or 4, and since there are 2 true labels, for sure 1 is true. This means that 2 has mixed coins. Moreover, there is a true label between 2 and 4. Thus, box 3 has a false label since there are 2 false ones, 1 is true, and one between 2 or 4 is true.

Since 3 lies, box 4 does not have all gold. But since 2 or 4 tells the truth, silver is in 3 or 1, that is, silver is not in 4. Then 4 also has mixed coins.

Box 2 & 4 are being contradictory by each claiming that two different boxes as containing all silver when it's known only one of it existed, so at least one of those must be lying. So at least one of Box 1 & 3 is telling the truth, but if both are truthful, then one of them must be containing all silver as claimed by Box 2 or 4 even though both of them should be lying (2 true labels vs 2 false labels), so this is impossible.

Now we know that one of Box 1 or 3 must have contained all silver, so Box 2 & 4 can't have that anymore. The possibilities for Box 2 & 4 is either all gold or mixed ones, but we know one of Box 1 & 3 is truly labelled and the other not, therefore Box 2 & Box 4 should either be both gold or both mixed, but we know that we have only one all gold but 2 mixed combo boxes, so we can easily reject the possibility of both all gold.

Conclusions :
Mixed combo ==> Boxes 2 & 4
All silver ==> Box 1 or Box 3
All gold ==> Box 3 or Box 1