C++ :

#define deb 0
#include <stdlib.h>
#include <algorithm>
#include <stdio.h>
#include <queue>
#include <set>
#include <string>
using namespace std;
typedef string board;

#define B(b,i,j) b[((i)*4)+(j)]

typedef struct {
    board b;
    int moves;
} mboard;

int bad(board b) {
    int j;
    for(int i = 0; i < 3; i++) for(j = 0; j < 4; j++) {
        if(B(b,i,j) == 'R' || B(b,i,j) == 'B')
            if(B(b,i+1,j) == 'R' || B(b,i+1,j) == 'B')
                return 1;
    }
    for(int i = 0; i < 4; i++) for(j = 0; j < 3; j++) {
        if(B(b,i,j) == 'R' || B(b,i,j) == 'B')
            if(B(b,i,j+1) == 'R' || B(b,i,j+1) == 'B')
                return 1;
    }
    return 0;
}

queue<mboard> q;
set<board> seen;

void print(board b) {
    for(int i = 0; i < 4; i++) {
    for(int j = 0; j < 4; j++) {
        printf("%c", B(b,i,j));
    }
        printf("\n");
    }
        printf("\n");
}

void attempt(board b, int moves) {
    if(seen.count(b) > 0) return;
    if(deb) puts("not seen");
    seen.insert(b);
    int s = seen.size();
    if(deb) if((s%1000) == 0) printf("seen: %u q: %u\n", seen.size(), q.size());
    if(deb) print(b);
    if(bad(b)) return;
    if(deb) puts("not bad");
    mboard m;
    m.b = b;
    m.moves = moves;
    q.push(m);
    if(deb) puts("pushed");
}

int badd(int i, int di) {
    if(i+di >3) return 1;
    if(i+di <0) return 1;
    return 0;
}
void move(board b, int i, int j, int di, int dj, int moves) {
    if(badd(i,di*2)) return;
    if(badd(j,dj*2)) return;
    if(B(b,i,j) == '.') return;
    if(B(b,i+di,j+dj) == '.') return;
    if(B(b,i+di+di,j+dj+dj) != '.') return;
    B(b,i+di+di,j+dj+dj) = B(b,i,j);
    B(b,i,j) = '.';
    attempt(b, moves+1);
}
void move2(board b, int i, int j, int di, int dj, int moves) {
    if(badd(i,di*3)) return;
    if(badd(j,dj*3)) return;
    if(B(b,i,j) == '.') return;
    if(B(b,i+di,j+dj) == '.') return;
    if(B(b,i+di+di,j+dj+dj) == '.') return;
    if(B(b,i+di+di+di,j+dj+dj+dj) != '.') return;
    B(b,i+di+di+di,j+dj+dj+dj) = B(b,i,j);
    B(b,i,j) = '.';
    attempt(b, moves+1);
}

int main() {
    int i,j;
    int pos=0;
    int mb=0;

    char line[100];

    board b = "................";
    for(i=0; i<4; i++) {
        gets(line);
        for(j=0; j<4; j++) B(b,i,j) = line[j];
    }
    attempt(b, 0);
    while(q.size() > 0) {
        pos++;
        mboard m = q.front();
        q.pop();
        board b = m.b;
        if(deb) if(m.moves > mb) {
            mb = m.moves;
            printf("moves: %u\n", mb);
        }
        if(B(b,0,0) == 'R') {
            printf("%u\n", m.moves);
            break;
        }
        for(i=0; i < 4; i++) for(j=0; j<4; j++) {
            move(b, i,j,0,1, m.moves);
            move(b, i,j,0,-1, m.moves);
            move(b, i,j,1,0, m.moves);
            move(b, i,j,-1,0, m.moves);
            move2(b, i,j,0,1, m.moves);
            move2(b, i,j,0,-1, m.moves);
            move2(b, i,j,1,0, m.moves);
            move2(b, i,j,-1,0, m.moves);
        }
    }
    if(deb) printf("done %u\n" , pos);
}