Mossy Stone Brick walls can be cut from Mossy Stone Bricks using a stonecutter. You can find Mossy Stone Bricks in Igloos, Ruined Portals, Cold Ocean Ruins (and also Strongholds), or you can craft them using Stone Bricks and Moss or Vines.
Igloo basements always generate with 17 Mossy Stone Bricks, shown highlighted in the screenshot. There is also 1 Infested Mossy Stone Bricks which will spawn a silverfish instead of dropping a block (without silk touch), shown by the silverfish (highlighted red).
If you are mining 6 to make the wall in a crafting table, it's best to just get them from the left side by the chest. If you have a stonecutter you only need 1.
Ruined portals can generate with Mossy Stone Bricks (and in one case, the Mossy Stone Brick Wall itself), which is exactly what you want for this goal. But not all RPs are created equally. The chance to replace blocks in the RP with Mossy Stone Bricks or the Wall depends on "Mossiness", which changes based on where the RP generated.
This table shows the chance for each RP to have at least 1 Mossy Stone Brick or Mossy Stone Brick Wall. Portal_8 (aka Big U) is the only one that can have walls, all the others assume a stonecutter.
Portal_2 and portal_5 both have Mossy Stone Bricks guaranteed, see below on where those are. All the others depend on "Mossiness", which is greatest in Oceans and Jungles (though Jungles have vines anyway), then Swamps, and other biomes follow.
Mossy Stone Bricks highlighted on Hanging Portal
Mossy Stone Bricks highlighted on L Portal
The walls highlighted in Big U
This video (left) goes over how you can get the Mossy Stone Bricks from Hanging Portal and L Portal, even in Deserts where they can be partially buried.
Portals are usually small (95% chance) but have a 5% chance to be one of the "giant" portals. The more stone bricks/chiseled stone bricks/stone an RP has, the greater the chance one of them is mossy. Each of these blocks have a 50% chance to be replaced, and then on top of that, a Mossiness% chance to be either Mossy Stone Bricks OR Mossy Stone Brick stairs. The stairs are unfortunately useless to us, which means a stone block in an 80% mossiness RP has a 20% chance of being a mossy stone brick.
Cold Ocean Ruins (not warm ones) have a chance to generate with Mossy Stone Bricks. Because of the order in which the game generates these, every Stone Brick in an Ocean Ruin has a 50% chance to be Mossy, 35% to be cracked, and 13.5% to remain as Stone Bricks.
You are therefore nearly guaranteed to get at least 1 Mossy Stone Brick from a cold ocean ruin. Even the smallest ocean ruin (see image) has a 99.8% chance to have at least 1 Mossy Stone Brick.
There are 4 ways of getting Moss: (1) Lush Cave, (2) Shipwrecks, (3) Trial Chamber, (4) Wandering Trader.
Lush Caves can be found under Azalea Trees or otherwise found using biome parameters, see this post in resources by Ducky. Also taken from Ducky's doc regarding finding lush caves:
"Based on these values, lush caves will never generate underneath badlands, eroded badlands, cherry groves, flower forests, ice spikes, plains, savannah, savannah plateau,snowy plains snowy slopes, sunflower plains, windswept hills or windswept gravelly hills. Predictably, most of the biomes with no trees can’t have lush caves underneath them. However, biomes without trees can have lush caves if the biome does not depend on humidity at all (-INF to +INF on the sheet). Lush caves can spawn under oceans, deserts, mushroom islands, beaches, and peak biomes because of this. It is best to just look for humidity over 0.2 instead of memorizing this list, since it is unintuitive. The depth value of 0.4 corresponds to about 51 blocks below the surface."
Shipwreck supply chests have a 42.1% chance to have Moss. Since only 70% of ships have a food chest, this means moss is a 29.47% chance per Shipwreck. If you're only needing moss for this goal, you can search oceans for Ocean Ruins, Ruined Portals and Shipwrecks. This makes oceans very strong for this goal.
Moss can come from two places in Trial Chambers, (1) Slime Trial Spawners, and (2) Supply chests in Hallways. Waiting on Sam for simulated averages, but Moss will roughly be a 25% chance per trial chamber. If you see one of the other small melee trial spawners (cave spider, silverfish, baby zombie) then you will not have a slime trial spawner. Supply chests can only be found in the "cache" part of hallways found through copper doors (see right).
The Wandering Trader has a 7% chance to sell Moss for 1 Emerald, if you somehow get to 20 minutes with this goal still on the board and one spawns.
Vines can be found in (1) Jungles, Swamps and Lush Caves, (2) Fallen Trees, (3) Pillager Outposts, (4) Trial Chambers.
Like above, see this post in resources for information regarding climate paramaters. Usually you can just think about whether you have a Swamp or Jungle nearby. You will need Shears (2 iron) to acquire vines, so weigh that against your other options for this goal.
Most relevantly, Oak Fallen Trees can have vines growing on the stumps. These fallen trees can generate in pretty much every biome that Oak Trees can generate.
Outposts overlay an "overgrown" version of the watchtower with structure integrity ~3%, meaning that on average, you will have 3.39 vines per outpost, and a 96.8% chance for at least 1 vine.
Vines can only be found in Trial Chambers if the Entrance room has a Mangrove tree. Per Trial Chamber, the chance of this happening is 22.2% per Trial Chamber. This means your chance to either have Moss or Vines from TCs for this goal is around 41.65%.