You should show more effort and paste some code, what you have tried. But anyhow, I think this is what you want:
// Collections
var mod1 = ee.ImageCollection("MODIS/006/MOD11A2");
var mod2 = ee.ImageCollection("MODIS/006/MOD13Q1");
// Some dates to filter
var d1 = ee.Date.fromYMD(2017,1,1)
var d2 = ee.Date.fromYMD(2017,3,1)
// filter collections and select needed bands
mod1 = mod1.filterDate(d1, d2).select('QC_Day')
mod2 = mod2.filterDate(d1, d2).select('NDVI')
// Use an equals filter to define how the collections match.
var filter = ee.Filter.equals({
leftField: 'system:index',
rightField: 'system:index'
});
// Create the join.
var simpleJoin = ee.Join.simple();
// Applt join
var mod1join = ee.ImageCollection(simpleJoin.apply(mod1, mod2, filter))
var mod2join = ee.ImageCollection(simpleJoin.apply(mod2, mod1, filter))
print('Joined', mod1join, mod2join)
var final_col = mod1join.map(function(img){
// Create a collection with 1 image
var temp = ee.ImageCollection(ee.List([img]));
// Apply join to collection 2
// Resulting collection will have 1 image with exact same date as img
var join = simpleJoin.apply(mod2join, temp, filter);
// Get resulting image
var i2 = ee.Image(join.first())
return img.addBands(i2)
})
print(final_col)