I downloaded the 1.10.2 of Project Red mod and some of the others mods that are needed for the Project Red Mechanical are at v1.7.10 and it is still crashing what is going on here is a report
---- Minecraft Crash Report ----

WARNING: coremods are present:
RebornCoreASM (RebornCore-1.10.2-2.13.5.136-universal.jar)
Contact their authors BEFORE contacting forge

// Hey, that tickles! Hehehe!

Time: 5/25/17 6:15 PM
Description: There was a severe problem during mod loading that has caused the game to fail

net.minecraftforge.fml.common.LoaderExceptionModCrash: Caught exception from RebornStorage (rebornstorage)
Caused by: java.lang.NoClassDefFoundError: RebornStorage/tiles/TileMultiCrafter
at RebornStorage.init.ModBlocks.init(ModBlocks.java:20)
at RebornStorage.RebornStorage.preinit(RebornStorage.java:36)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
at java.lang.reflect.Method.invoke(Unknown Source)
at net.minecraftforge.fml.common.FMLModContainer.handleModStateEvent(FMLModContainer.java:600)
at sun.reflect.GeneratedMethodAccessor4.invoke(Unknown Source)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
at java.lang.reflect.Method.invoke(Unknown Source)
at com.google.common.eventbus.EventSubscriber.handleEvent(EventSubscriber.java:74)
at com.google.common.eventbus.SynchronizedEventSubscriber.handleEvent(SynchronizedEventSubscriber.java:47)
at com.google.common.eventbus.EventBus.dispatch(EventBus.java:322)
at com.google.common.eventbus.EventBus.dispatchQueuedEvents(EventBus.java:304)
at com.google.common.eventbus.EventBus.post(EventBus.java:275)
at net.minecraftforge.fml.common.LoadController.sendEventToModContainer(LoadController.java:243)
at net.minecraftforge.fml.common.LoadController.propogateStateMessage(LoadController.java:221)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
at java.lang.reflect.Method.invoke(Unknown Source)
at com.google.common.eventbus.EventSubscriber.handleEvent(EventSubscriber.java:74)
at com.google.common.eventbus.SynchronizedEventSubscriber.handleEvent(SynchronizedEventSubscriber.java:47)
at com.google.common.eventbus.EventBus.dispatch(EventBus.java:322)
at com.google.common.eventbus.EventBus.dispatchQueuedEvents(EventBus.java:304)
at com.google.common.eventbus.EventBus.post(EventBus.java:275)
at net.minecraftforge.fml.common.LoadController.distributeStateMessage(LoadController.java:145)
at net.minecraftforge.fml.common.Loader.preinitializeMods(Loader.java:614)
at net.minecraftforge.fml.client.FMLClientHandler.beginMinecraftLoading(FMLClientHandler.java:257)
at net.minecraft.client.Minecraft.func_71384_a(Minecraft.java:439)
at net.minecraft.client.Minecraft.func_99999_d(Minecraft.java:351)
at net.minecraft.client.main.Main.main(SourceFile:124)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
at java.lang.reflect.Method.invoke(Unknown Source)
at net.minecraft.launchwrapper.Launch.launch(Launch.java:135)
at net.minecraft.launchwrapper.Launch.main(Launch.java:28)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
at java.lang.reflect.Method.invoke(Unknown Source)
at org.multimc.onesix.OneSixLauncher.launchWithMainClass(OneSixLauncher.java:236)
at org.multimc.onesix.OneSixLauncher.launch(OneSixLauncher.java:297)
at org.multimc.EntryPoint.listen(EntryPoint.java:162)
at org.multimc.EntryPoint.main(EntryPoint.java:53)
Caused by: java.lang.ClassNotFoundException: RebornStorage.tiles.TileMultiCrafter
at net.minecraft.launchwrapper.LaunchClassLoader.findClass(LaunchClassLoader.java:191)
at java.lang.ClassLoader.loadClass(Unknown Source)
at java.lang.ClassLoader.loadClass(Unknown Source)
... 46 more
Caused by: java.lang.NoClassDefFoundError: com/raoulvdberge/refinedstorage/api/autocrafting/ICraftingPatternContainer
at java.lang.ClassLoader.defineClass1(Native Method)
at java.lang.ClassLoader.defineClass(Unknown Source)
at java.security.SecureClassLoader.defineClass(Unknown Source)
at net.minecraft.launchwrapper.LaunchClassLoader.findClass(LaunchClassLoader.java:182)
... 48 more
Caused by: java.lang.ClassNotFoundException: com.raoulvdberge.refinedstorage.api.autocrafting.ICraftingPatternContainer
at net.minecraft.launchwrapper.LaunchClassLoader.findClass(LaunchClassLoader.java:191)
at java.lang.ClassLoader.loadClass(Unknown Source)
at java.lang.ClassLoader.loadClass(Unknown Source)
... 52 more
Caused by: java.lang.NullPointerException
at net.minecraft.launchwrapper.LaunchClassLoader.findClass(LaunchClassLoader.java:182)
... 54 more

This isn't project red, Seems RebornStorage is having issues, likely you don't have the correct version of Refined Storage installed. Paging @modmuss50