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Use these hints if you're stuck. Try solving on your own first.
Consider using dynamic programming.
Let dp[i][0] (dp[i][1]) be the length of the longest non-decreasing ending with nums1[i] (nums2[i]).
Initialize dp[i][0] to 1. If nums1[i] >= nums1[i - 1] then dp[i][0] may be dp[i - 1][0] + 1. If nums1[i] >= nums2[i - 1] then dp[i][0] may be dp[i - 1][1] + 1. Perform a similar calculation for nums2[i] and dp[i][1].